SUMMARYA stochastic representation of random error associated with parametrized physical processes ('stochastic physics') is described, and its impact in the European Centre for Medium-Range Weather Forecasts Ensemble Prediction System (ECMWF EPS) is discussed. Model random errors associated with physical parametrizations are simulated by multiplying the total parametrized tendencies by a random number sampled from a uniform distribution between 0.5 and 1.5. A number of diagnostics are described and a choice of parameters is made. It is shown how the scheme increases the spread of the ensemble, and improves the skill of the probabilistic prediction of weather parameters such as precipitation. A choice of stochastic parameters is made for operational implementation. The scheme was implemented successfully in the operational ECMWF EPS on 21 October 1998.