A pencil beam model for the calculation of the lateral scattering in water of protons for any therapeutic energy and depth is presented. It is based on the full Molière theory, taking into account the energy loss and the effects of mixtures and compounds. Concerning the electromagnetic part, the model has no free parameters and is in very good agreement with the FLUKA Monte Carlo (MC) code. The effects of the nuclear interactions are parametrized with a two-parameter tail function, adjusted on MC data calculated with FLUKA. The model, after the convolution with the beam and the detector response, is in agreement with recent proton data in water from HIT. The model gives results with the same accuracy of the MC codes based on Molière theory, with a much shorter computing time.