Persistent controversies about human multiple task performance suggest that research on it will benefit from increased use of precise computational models. Toward this objective, the present report outlines a comprehensive theoretical framework for understanding and predicting the performance of concurrent perceptual motor and cognitive tasks. The framework involves an Executive Process Interactive Control (EPIC) architecture, which has component modules that process information at perceptual, cognitive, and motor levels. On the basis of EPIC, computational models that use a production system formalism may be constructed to simulate multiple task performance under a variety of conditions. These models account well for reaction time data from representative paradigms such as the psychological refractory period (PRP) procedure. With modest numbers of parameters, good fits between empirical and simulated reaction times support several key conclusions: (1) at a cognitive level, people can apply distinct sets of production rules simultaneously for executing the procedures of multiple tasks; (2) there is no immutable central response selection or decision bottleneck; (3) people's capacity to process information and take action at peripheral perceptual motor levels is limited; (4) to cope with such limits and to satisfy task priorities, flexible scheduling strategies are used; (5) these strategies are mediated by executive cognitive processes that coordinate concurrent tasks adaptively. The initial success of EPIC and models based on it suggest that they may help characterize multiple task performance across many domains, including ones that have substantial practical relevance.