Accurate prediction of the intensity and variability of strong ground motions from future large earthquakes depends on our ability to simulate realistic earthquake source models. We have developed a procedure to generate physically consistent earthquake-rupture models that should help make such simulations more accurate. We term these models “pseudo dynamic” because they are kinematic models that are designed to emulate important characteristics of dynamic rupture. We construct pseudo-dynamic models first by generating a slip distribution as a realization of a spatial random field that is consistent in its scaling and spatial variability with slip distributions observed in past earthquakes. We then compute the static stress drop associated with the slip distribution, which in turn is used to estimate the temporal evolution of slip through a set of empirical relationships derived from the analysis of spontaneous rupture models. Finally, a simple energy-budget calculation is used to eliminate models that are not likely to propagate spontaneously. The principal advantage of the pseudo-dynamic approach is that it avoids the computational demands of generating fully dynamic rupture models for multiple realizations of a scenario earthquake. While the relationships between source parameters described in this paper are simplifications of the true complexity of the physics of rupture, they help identify important interactions between source properties that are relevant for strong ground motion prediction, and should provide an improvement over purely kinematic models.