A model that accounts for the essential mechanisms of pellet acceleration by two-stage guns is described. Gas compression inside the second stage is assumed to be zero-dimensional, while pellet acceleration is considered one-dimensional unsteady and is solved by the method of characteristics. The coupling between the two parts is explicit. An ideal gas equation of state is used for the entire system. Numerical results are compared with available analytical solutions. A sensitivity analysis showing the influence of many parameters is performed. Comparisons with experimental results are satisfactory, as better than qualitative agreement was obtained. The model was found to be sufficiently reliable and suitable for preliminary studies on different operating conditions and geometries in order to save time and experimental resources.