In this paper a multidimensional method is described and evaluated for the prediction of Diesel sprays. The method, which shares many features with similar approaches developed elsewhere, embodies an Eulerian description of the gas flow and a stochastic Lagrangian treatment of the spray droplets. Gas phase turbulence effects are represented by the k-ε model and their influence on the droplets is modelled stochastically, as are the processes of collision and coalescence. Comparisons are made with the spray penetration measurements in a quiescent bomb of Yule et al  covering a range of pressures and temperatures. Satisfactory agreement is obtained at combinations of low pressure and temperature and high pressure and temperature, but not for high-pressure, low-temperature cases. The sensitivity of the predicted penetration rates to the assumed initial droplet size distribution is relatively weak, but the calculated vaporization rates are strongly sensitive. This demonstrates the inadequacy of penetration data as a testing-ground for spray models and points to a need for (a) an atomisation model and (b) vaporization data.