In this talk I will present my dissertation prospectus, which deals with theoretical phonology of word stress. I focus on the prosodic system of Abkhaz ([abk] Northwest Caucasian, Abkhazia), which I use to evaluate predictions between theoretical approaches to prosody. The empirical core of the dissertation will comprise acoustic analyses of how stress is realized, as well as corpus analyses of stress alternations across the lexicon. These will form the basis for a phonological analysis of Abkhaz stress. The talk will focus on the subpart of the dissertation which concerns stress-bearing units (SBUs) in Abkhaz. Which units host stress at the underlying level, and are these the same as the SBUs in surface representations? I outline the phonetic and phonological studies I will conduct to answer these questions. I also connect the data to theoretical work claiming that the syllable is the only possible SBU (Hayes 1995, Hyman 2006), something which previous work (Andersson 2020) argues might be false for Abkhaz.