A new model has been introduced to characterize the action of a fluid phase enzyme on a solid phase substrate. This approach is applied to evaluate the kinetics of fibrin dissolution with several proteases. The model predicts the rate constants for the formation and dissociation of the protease-fibrin complex, the apparent order of the association reaction between the enzyme and the substrate, as well as a global catalytic constant (kcat) for the dissolution process. These kinetic parameters show a strong dependence on the nature of the applied protease and on the structure of the polymerized substrate. The kinetic data for trypsin, PMN-elastase, and three plasminogen-derived proteases with identical catalytic domain, but with a varied N-terminal structure, are compared. The absence of kringle5 in des-kringle1-5-plasmin (microplasmin) is related to a markedly lower kcat (0.008 s-1) compared with plasmin and des-kringle1-4plasmin (miniplasmin) (0.039 s-1). The essentially identical kinetic parameters for miniplasmin and plasmin with the exception of kdiss, which is higher for miniplasmin (81.8 s-1 versus 57.6 s-1), suggest that the first four kringle domains are needed to retain the enzyme in the enzyme-fibrin complex. Trypsin, a protease of similar primary specificity to plasmin, but with a different catalytic domain, shows basically the same kcat as plasmin, but its affinity to fibrin is markedly lower compared with plasmin and even microplasmin. The latter suggests that in addition to the kringle domains, the structure of the catalytic domain in plasmin also contributes to its specificity for fibrin. The thinner and extensively branched fibers of fibrin are more efficiently dissolved than the fibers with greater diameter and lower number of branching points. When the polymer is stabilized through covalent cross-linking, the kcat for plasmin and miniplasmin is 2-4-fold higher than on non-cross-linked fibrin, but the decrease in the association rate constant for the formation of enzyme-substrate complex explains the relative proteolytic resistance of the cross-linked fibrin. Thus, the functional evaluation of the discrete steps of the fibrinolytic process reveals new aspects of the interactions between proteases and their polymer substrate.