A three-dimensional numerical model for mountain waves is described and validated against radiosonde observations over the Isle of Arran, south-west Scotland. The model is based on the Boussinesq equations of motion linearised about a background profile of wind, potential temperature and density. The equations are discretised using finite-difference approximations and the time dependence is retained. Solutions are then computed by integrating forward the equations in time until a stationary mountain-wave field is obtained. Data from radiosondes, launched during fieldwork on Arran during February and March 2000, are used to represent the background flow and model simulations of the wave field are compared directly with fluctuations in the ascent rates of the balloons. On average, the model reproduces the observed maximum peak-to-peak vertical velocity to within about 0.6 ms-1. In many cases the accuracy of the simulations is even better than this: the model vertical velocity along the path of the radiosondes agree well with fluctuations in the balloon ascent rate. The sensitivity of the model results to the wave ‘launching height’ is discussed. The model was also used to provide forecasts of wave activity during the field campaign. In this case, rather than using radiosonde data to represent the background flow, data were extracted from a global forecast model. The accuracy of these forecasts is examined and the viability of using such a model to provide routine operational high-resolution mountain-wave forecasts for specific sites is discussed.