This is based on possibly outmoded English public school tradition. See the link cited below. It may, of course, not suit your context at all. Alternatively, Rasmus one, Rasmus two, Rasmus three might do the trick.

I see no problem here, your version is OK.

It definitely wasn't Zeus, he was the youngest of the three brothers, Poseidon was the middle child, and Hades was the eldest(oldest) of the three, but they all ...
wiki.answers.com/.../Who_is_the_oldest_Poseidon_Zeus_or_Hades


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Note added at 1 hr (2013-09-10 07:01:04 GMT)
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I would probably use articles: the Eldest Rasmus, the Middle Rasmus, the Youngest Rasmus.

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Note added at 1 hr (2013-09-10 07:07:00 GMT)
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Typically, researchers classify siblings as "eldest", "middle child", and "youngest" or simply distinguish between "firstborn" and "later born" children.
http://en.wikipedia.org/wiki/Sibling

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Note added at 1 hr (2013-09-10 07:39:07 GMT)
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She stands at the tsar's left with the eldest and the youngest Ivans the next day.
Marya Morevna towers even over the middle Ivan, who is by far the largest and strongest of the three brothers.
http://archiveofourown.org/works/607985

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Note added at 2 hrs (2013-09-10 07:47:57 GMT)
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OK, what about these:
Big Rasmus
Second Rasmus / Just Rasmus / Rasmus
Little Rasmus
???

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Note added at 2 hrs (2013-09-10 07:49:43 GMT)
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ИЛИ:
Big Rasmus
Younger Rasmus
Little Rasmus

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Note added at 2 hrs (2013-09-10 07:50:24 GMT)
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По-моему, последний вариант - хоть куда! :)

Perhaps a work around.

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Note added at 1 hr (2013-09-10 07:25:47 GMT)
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A tricky dilemma indeed.

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Note added at 1 hr (2013-09-10 07:30:54 GMT)
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The only other variant I can think of would be "Rasmus in the middle" a la "Malcolm in the middle."

The titular Malcolm is the frustrated and eternally-perplexed "middle" child of a middle-class home who is discovered to have a genius-level IQ.

http://tvtropes.org/pmwiki/pmwiki.php/Series/MalcolmInTheMid...

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Note added at 2 hrs (2013-09-10 08:24:23 GMT)
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For instance one might say "the middle John" to emphasize that John from other Johns. Or "the middle John" may be a created name to distinguish from other Johns. However, used in a descriptive way or in a comparative sense, you would probably say "The Eldest John", "John the middle child" and "the youngest John."

It all depends on whether the author is using the terms to refer to a name of the character or if he is describing/contrasting the characters relationship to one another.

i.e. (descriptive) John, the middle child, went as far as 9th grade. Charles Jr., the oldest, made it to the 10th.
http://www.brucegoldfarb.com/lives.htm

(nominal) While it was not uncommon for people to name their children after their deceased siblings, John Warren's two sons, both named John, were alive at the same time. To distinguish between them, the eldest John was called "the elder" while the second John, the middle child, was called John "the middle." Perhaps John the Elder was a sickly child and wasn't expected to live at the time of John the Middle's birth five years later. John Warren and his wife may have wanted to ensure that at least one of their sons survived with the name.
http://homepages.rootsweb.ancestry.com/~sam/jwarren/john.htm...


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Note added at 2 hrs (2013-09-10 08:40:46 GMT)
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Or possibly along the same lines of what Andrew Vdovin said...maybe you can use Rasmus, Rasmus's younger brother and Rasmus's older brother. Again it depends on whether Расмус старший would refer to the actual name of the character or title or merely be describing the relationship to Rasmus himself. Personally, I think it would be the later.

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Note added at 3 hrs (2013-09-10 08:54:59 GMT)
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I agree with katerina turevich, "puting it in front of the name. Older, middle, younger Rasmus. \"the older Rasmus said: ...\'the younger Rasmus turned a samersault\', while the middle brother was making porridge. yeah, it\'s a bit too repetitive." Perhaps the best solution would be not to use any single suggestion exclusively but to vary the references throughout the story.

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Note added at 3 hrs (2013-09-10 09:14:27 GMT)
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Again, depending on whether the author is implying that Rasmus is the name of the characters or describing their relationship to each other. In the first case I think you would have to go with something like "Rasmus the middle" or as Andrew Vdovin said "The middle Rasmus." If it is the later case, then you I think you could vary the description (the younger Rasmus, Rasmus 1, Rasmus's younger brother, Rasmus the middle child, etc.)

Mark, this is not so much about translation, as I am sure you realize, as about good writing style. That said, I'd go with something purely contextual, like the above, possibly omitting the name of Rasmus altogether where it doesn't fit the rhythm. Then, on other occasions you can definitely say Rasmus the middle, or simply the middle son, the simpler the better. Middle Rasmus sounds a bit weird to my ears. All those other complicated ranking schemes some folks offer here strike me as a little unwieldy and unworkable stylistically. I say improvise as you go along, recycling the more successful solutions every now and then. After all, who gives a hoot what the original actually says? What matters - and sells! - is good flow and readability.