Microsimulation is fast becoming the approach of choice for modelling and analysing complex processes in the absence of mathematical tractability. While this approach has been developed and promoted in engineering contexts for some time, it has more recently found a place in the mainstream of the study of chronic disease interventions such as cancer screening. The construction of a simulation model requires the specification of a model structure and sets of parameter values, both of which may have a considerable amount of uncertainty associated with them. This uncertainty is rarely quantified when reporting microsimulation results. We suggest a Bayesian approach and assume a parametric probability distribution to mathematically express the uncertainty related to model parameters. First, we design a simulation experiment to achieve good coverage of the parameter space. Second, we model a response surface for the outcome of interest as a function of the model parameters using the simulation results. Third, we summarize the variability in the outcome of interest, including variation due to parameter uncertainty, using the response surface in combination with parameter probability distributions. We illustrate the proposed method with an application of a microsimulator designed to investigate the effect of prostate specific antigen (PSA) screening on prostate cancer mortality rates.