An important application of cognitive architectures is to provide human performance models that capture psychological mechanisms in a form that can be “programmed” to predict task performance of human-machine system designs. While many aspects of human performance have been successfully modeled in this approach, accounting for multi-talker speech task performance is a novel problem. This paper presents a model for performance in a two-talker task that incorporates concepts from the psychoacoustic study of speech perception, in particular, masking effects and stream formation.