The gantry for proton radiotherapy at the Paul Scherrer Institute (PSI) is designed specifically for the spot-scanning technique. Use of this technique to its full potential requires dose calculation algorithms which are capable of precisely simulating each scanned beam individually. Different specialized analytical dose calculations have been developed, which attempt to model the effects of density heterogeneities in the patient's body on the dose. Their accuracy has been evaluated by a comparison with Monte Carlo calculated dose distributions in the case of a simple geometrical density interface parallel to the beam and typical anatomical situations. A specialized ray casting model which takes range dilution effects (broadening of the spectrum of proton ranges) into account has been found to produce results of good accuracy. This algorithm can easily be implemented in the iterative optimization procedure used for the calculation of the optimal contribution of each individual scanned pencil beam. In most cases an elemental pencil beam dose calculation has been found to be most accurate. Due to the long computing time, this model is currently used only after the optimization procedure as an alternative method of calculating the dose.