Numerical simulations have been obtained for two-dimensional laminar flows past a circular cylinder in the transitional regime. Computations are performed using the direct simulation Monte Carlo method for Knudsen numbers of 0.02 and 0.2 and Mach numbers of 0.102 and 0.4. For these conditions, Reynolds number ranges from 0.626 to 24.63 and the flows are steady. Results show that separation occurs in the wake region for the flow with Mach number of 0.4 and Knudsen number of 0.02, but for the other eases flows are attached. The effects of flow speed, rarefaction, domain size and the outflow boundary conditions are investigated. Results show sensitivity to the domain size and the outflow boundary conditions in the low Mach number calculations, but as the speed increases the sensitivity decreases. Although no experimental data are available for direct comparison, the present calculations are found to be in very good agreement with the findings of other researchers.