We report on a technique for modelling biological systems based on the ntcc calculus, a model of concurrency where systems are specified by means of constraints (i.e., formulae in logic). We show that the ability of ntcc to express partial information, concurrency, non-determinism and timed behaviour makes it wellsuited model and simulate biochemical reactions networks. Based on this technique, we introduce BioWayS (BIOchemical pathWAY Simulator), a software tool for the quantitative modelling and analysis of biological systems. We show the applicability of BioWayS in the context of two well-studied biological systems: the glycogen breakdown pathway and the life cycle of the human immunodeficiency virus.