Blood clot contraction (retraction) is driven by platelet-generated forces propagated by the fibrin network and results in clot shrinkage and deformation of erythrocytes. To elucidate the mechanical nature of this process, we developed a model that combines an active contractile motor element with passive viscoelastic elements. Despite its importance for thrombosis and wound healing, clot contraction is poorly understood. This model predicts how clot contraction occurs due to active contractile platelets interacting with a viscoelastic material, rather than to the poroelastic nature of fibrin, and explains the observed dynamics of clot size, ultrastructure, and measured forces. Mechanically passive erythrocytes and fibrin are present in series and parallel to active contractile cells. This mechanical interplay induces compressive and tensile resistance, resulting in increased contractile force and a reduced extent of contraction in the presence of erythrocytes. This experimentally validated model provides the fundamental mechanical basis for understanding contraction of blood clots.