This paper aims to introduce and examine two Japanese translations of Finnegans Wake which has been considered to be "untranslatable" or one of the most difficult books to translate. But now we can enjoy it in many languages--Franch, German, Spanish, Italian, Dutch, Japanese, Korean, etc. The basic language of FW is doubtlessly English, and most of the dominant languages are European. Naoki Yanase, the Japanese translator was challenged to complete his translation into Japanese (1991-1993). Of course some of the rich ambiguity of the original may have been lost, but he made a great effort to convey the atmosphere and tone of the original: he even translated "Joyce`s style" into Japanese. Yanase`s translation is a novel in its own right and a great masterpiece of Japanese literature. In June 2004, another translator, Kyoko Niyata, published a more readable Japanese translation of FW. Her abridged translation (about half the size of the original) with her detailed notes, is much more understandable than Yanase`s, and plays another role for prospective Japanese readers. Comparing these two Japanese translations, we can understand these two effective methods to convey the ambiguities of Joycean words in Finnegans Wake in translation.