Intrinsic tenase consists of activated Factors IX (IXa) and VIII (VIIIa) assembled on a negatively charged phospholipid surface. In vivo, this surface is mainly provided by activated platelets. In vitro, phosphatidylcholine/phosphatidylserine vesicles are often used to mimic natural pro-coagulant membranes. In the present study, we developed a quantitative mathematical model of Factor X activation by intrinsic tenase. We considered two situations, when complex assembly occurs on either the membrane of phospholipid vesicles or the surface of activated platelets. On the basis of existing experimental evidence, the following mechanism for the complex assembly on activated platelets was suggested: (i) Factors IXa, VIIIa and X bind to their specific platelet receptors; (ii) bound factors form complexes on the membrane: platelet-bound Factor VIIIa provides a high-affinity site for Factor X and platelet-bound Factor IXa provides a high-affinity site for Factor VIIIa; (iii) the enzyme–cofactor–substrate complex is assembled. This mechanism allowed the explanation of co-operative effects in the binding of Factors IXa, VIIIa and X to platelets. The model was reduced to obtain a single equation for the Factor X activation rate as a function of concentrations of Factors IXa, VIIIa, X and phospholipids (or platelets). The equation had a Michaelis–Menten form, where apparent Vmax and Km were functions of the factors’ concentrations and the internal kinetic constants of the system. The equation obtained can be used in both experimental studies of intrinsic tenase and mathematical modelling of the coagulation cascade. The approach of the present study can be applied to research of other membrane-dependent enzymic reactions.