In this paper we developed a Stochastic Petri Net (SPN) based model to introduce uncertainty to capture the variability of biological systems. The coagulation cascade, one of the most complex biochemical networks, has been widely analyzed in literature mostly with ordinary differential equations, outlining the general behavior but without pointing out the intrinsic variability of the system. Moreover, the computer simulation allows the assessment of the reactions over a broad range of conditions and provides a useful tool for the development and management of several observational studies, potentially customizable for each patient. We describe the SPN model for the Tissue Factor induced coagulation cascade, more intuitive and suitable than models hitherto appeared in the literature in terms of bioclinical manageability. The SPN has been simulated using Tau-Leaping Stochastic Simulation Algorithm, and in order to simulate a large number of models, to test different scenarios, we perform them using High Performance Computing. We analyze different settings for model representing the cases of "healthy" and "unhealthy" subjects, comparing their average behavior, their inter- and intra-variability in order to gain valuable biological insights.