Omission has a multifaceted nature with regards to literary translation. It functions as a cohesive device represented in ellipsis, as a literary device, and as a translation strategy. Ellipsis, as both a cohesive device and a literary device in a text, poses a challenge for the literary translator who is to render faithfully the author's style and the identity of the text. On the other hand, literary translators may resort to omission as a translation strategy to overcome specific translation problems. This paper aims at investigating this multifaceted nature of omission and foregrounding its role as both a problem and a solution in literary translation. The corpus of the study is taken from Hemingway's Hills Like White Elephants and Joyce's The Sisters which are known with their frequent use of ellipsis. Categorization of ellipsis in this study is based on Halliday and Hasan (1976), Quirk et al. (1985), and Biber et al. (1999). The paper also studies the translation strategies used to overcome omission as a problem, and at the same time, analyzes the use of omission to overcome other translation problems. The results show that literary translators mostly resort to four translation strategies when translating omission. Such strategies should be cautiously used; otherwise they may have adverse effects. The same rule applies to the use of omission as a translation strategy.