The propensity functions of the Stochastic Simulation Algorithm (SSA) have been derived under the point-molecule assumption, i.e., that the total volume of the molecules is negligible compared to the volume of the container. In this paper we investigate the impact of relaxing the point-molecule assumption. We report results of computational experiments on systems of N hard discs of diameter l moving ballistically inside finite two-dimensional containers. Since the SSA requires that inter-reaction times be exponentially distributed, we study the distribution of times t between when the system is initialized in a well-stirred state and when the first inter-molecular collision occurs. We find the t-distribution to be well approximated by an exponential distribution, with deviations from exponentiality becoming apparent in systems with small numbers of molecules in the limits of very low and very high area density (defined as the ratio of the area of the molecule disks to the total area of the system). As expected, when 0 l ® the impact of the area excluded by the molecules on the t-distribution is negligible. For high area density it appears that the molecules effectively exclude an area which starts out greater than the close-packed area of their disks, for systems with few molecules, but approaches the close-packed area as the number of molecules increases. This suggests that the effect of reactant-excluded volume on reaction kinetics in dense, finite, two and three dimensional systems may be underestimated, and underlines the importance of studying it further.