This dissertation proposes a model of word stress in a derivational version of Optimality Theory (OT) called Harmonic Serialism (HS; Prince and Smolensky 1993/2004, McCarthy 2000, 2006, 2010a). In this model, the metrical structure of a word is derived through a series of optimizations in which the 'best' metrical foot is chosen according to a ranking of violable constraints. Like OT, HS models cross-linguistic typology under the assumption that every constraint ranking should correspond to an attested language. Chapter 2 provides an argument for modeling stress typology in HS by showing that the serial model correctly rules out stress patterns that display non-local interactions, while a parallel OT model with the same constraints and representations fails to make such a distinction. Chapter 3 discusses two types of primary stress---autonomous and parasitic---and argues that limited parallelism in the assignment of primary stress is warranted by a consideration of attested typology. Stress systems in which the primary stress appears to behave autonomously from secondary stresses require that primary stress assignment be simultaneous with a foot's construction. As a result, a provision to allow primary stress to be reassigned during a derivation is necessary to account for a class of stress systems in which primary stress is parasitic on secondary stresses. Chapter 4 takes up two issues in the definition of constraints on primary stress, including a discussion of how primary stress alignment should be formulated and the identification of vacuous satisfaction as a cause of problematic typological predictions. It is proposed that all primary stress constraints be redefined according to non-vacuous schemata, which eliminate the problematic predictions when implemented within HS. Finally, chapter 5 considers the role of representational assumptions in typological predictions with comparisons between HS and parallel OT. The primary conclusion of this chapter is that constituent representations (i.e., feet) are necessary in HS to account for rhythmic stress patterns in a typologically restrictive way.