This dissertation is an investigation of the stress system of Squamish (Skwxwú7mesh), one of ten languages that make up the Central division of the Northwest Coast branch of Salishan, a linguistic group indigenous to the Pacific Northwest region of North America. Although other researchers have previously investigated aspects of stress in the language, this work provides the first integrated account of the Squamish stress system as a whole, couched in an Optimality Theoretic framework. The first two chapters are introductory, with Chapter 1 supplying a contextual background for the undertaking within linguistics, and especially within Salishan linguistices, while Chapter 2 provides a thorough grounding in the phonology and phonemics of Squamish in particular. Chapter 3 begins the formal analysis of stress in Squamish by examining the way stress surfaces in free root morphemes,which tend to stress penultimate syllables whenever they contain either a full vowel or a schwa followed by a resonant consonant. Given this outcome, Chapter 4 continues the investigation of basic stress patterns by looking more closely at the interactive roles of schwa, sonority, weight and the structure of syllables and feet in Squamish stress assignment. With the basic stress pattern established, the remaining chapters look at the outcome of stress in morphologically complex Squamish words. Thus, Chapter 5 is an analysis of stress in words involving prefixation, especially those resulting from CVC and CV prefixal reduplication, since non-reduplicative prefixes are unstressable; and Chapters 6 and 7 investigate the occurrence of stress in polymorphemic words resulting from the addition of lexical suffixes and grammatical suffixes, respectively. While stress in roots is generally predictable on the basis of phonological factors alone, that in polymorphemic words may also be influenced by morphological factors, as when a root or suffix has underlying lexical accent, and such factors then take precedence ofer phonological factors. In addition, prosodic domains play an important and interactive work.