The detailed kinetic model of Prostaglandin H Synthase-1 (COX-1) was developed to in silico test and predict inhibition effects of nonsteroidal anti-inflammatory drugs (NSAIDs) on target. The model takes into account key features of the complex catalytic mechanism of cyclooxygenase-1, converting arachidonic acid to prostaglandin PGH(2), and includes the description of the enzyme interaction with various types of NSAIDs (reversible/irreversible, non-selective and selective to COX-1/COX-2). Two different versions of the model were designed to simulate the inhibition of COX-1 by NSAIDs in two most popular experimental settings - in vitro studies with purified enzyme, and the experiments with platelets. The developed models were applied to calculate the dose-dependence of aspirin and celecoxib action on COX- 1 in vitro and in vivo conditions. The mechanism of the enhancement of aspirin efficiency in platelet as compared to its action on purified COX-1 was elucidated. The dose-dependence of celecoxib simulated with the use of the "in vivo" version of the model predicted potentially strong inhibitory effect of celecoxib on thromboxan production in platelets. Simulation of the combined effect of two NSAIDs, aspirin and celecoxib, on COX-1 allowed us to reveal the mechanism underlying the suppression of aspirin-mediated COX-1 inhibition by celecoxib. We discuss our modelling results in the context of the on-going debates on the potential cardio-vascular risks associated with co-administration of various types of NSAIDs.