Thrombosis is a life-threatening clinical condition characterized by the obstruction of blood flow in a vessel due to the formation of a large thrombus. The pathogenesis of thrombosis is complex because the type of formed clots depends on the location and function of the corresponding blood vessel. To explore this phenomenon, we develop a novel multiscale model of platelet-fibrin thrombus growth in the flow. In this model, the regulatory network of the coagulation cascade is described by partial differential equations. Blood flow is introduced using the Navier–Stokes equations and the clot is treated as a porous medium. Platelets are represented as discrete spheres that migrate with the flow. Each platelet can attach to the thrombus, aggregate, become activated, express proteins on its surface, detach, and/or become non-adhesive. The interaction of platelets with blood flow is captured using the Immersed Boundary Method (IBM). We use the model to investigate the role of flow conditions in shaping the dynamics of venous and arterial thrombi. We describe the formation of red and white thrombi under venous and arterial flow respectively and highlight the main characteristics of each type. We identify the different regimes of normal and pathological thrombus formation depending on flow conditions. © 2019 Elsevier Ltd