To better understand the mechanisms leading to the formation and growth of mural thrombi on biomaterials, we have developed a two-dimensional computational model of platelet deposition and activation in flowing blood. The basic formulation is derived from prior work by others, with additional levels of complexity added where appropriate. It is comprised of a series of convection-diffusion-reaction equations which simulate platelet-surface and platelet-platelet adhesion, platelet activation by a weighted linear combination of agonist concentrations, agonist release and synthesis by activated platelets, platelet-phospholipid-dependent thrombin generation, and thrombin inhibition by heparin. The model requires estimation of four parameters to fit it to experimental data: shear-dependent platelet diffusivity and resting and activated platelet-surface and platelet-platelet reaction rate constants. The model is formulated to simulate a wide range of biomaterials and complex flows. In this article we present the basic model and its properties; in Part II (Sorensen et al., Ann. Biomed. Eng. 27:449-458, 1999) we apply the model to experimental results for platelet deposition onto collagen.