Untranslatability constitutes one of the controversial issues within the area of Translation Studies. Scholars frequently disagree as it its very existence, some of them claiming that certain linguistic effects simply cannot be translated into another language, while other asserting that all texts produced by man are translatable to a greater or lesser degree, irrespective of the linguistic means they apply. The purpose of this paper is, first of all, to illustrate the issue of potential untranslatability by presenting a Spanish text featuring a plethora of challenging linguistic effects, and then attempt to translate its fragments into two languages: English and Polish. The paper also discusses the problems encountered during the very translation process, as well as the solutions selected together with their justifications. All this is done with a view to concluding whether untranslatability exists indeed, or whether the challenging linguistic effects present in a text can be successfully reproduced in another language.