Various fields of application, such as risk assessments of the insurance industry or the design of flood protection systems, require reliable precipitation statistics in high spatial resolution, including estimates for events with high return periods. Observations from point stations, however, lack of spatial representativeness, especially over complex terrain. Current numerical weather models are not capable of running simulations over thousands of years. This paper presents a new method for the stochastic simulation of widespread precipitation based on a linear theory describing orographic precipitation and additional functions that consider synoptically driven rainfall and embedded convection in a simplified way. The model is initialized by various statistical distribution functions describing prevailing atmospheric conditions such as wind vector, moisture content, or stability, estimated from radiosonde observations for a limited sample of observed heavy rainfall events. The model is applied for the stochastic simulation of heavy rainfall over the complex terrain of southwestern Germany. It is shown that the model provides reliable precipitation fields despite its simplicity. ... mehrThe differences between observed and simulated rainfall statistics are small, being of the order of only ±10 % for return periods of up to 1000 years.