We analyze the grain size distribution during solid phase crystallization of Silicon thin films. We use a model developed recently that offers analytical expressions for the time-evolution of the grain size distribution during crystallization of a d-dimensional solid. Contrary to the usual fit of the experimental results with a lognormal distribution, the theory describes the data from basic physical principles such as nucleation and growth processes. The theory allows for a good description of the grain size distribution except for early stages of crystallization. The latter case is expected and discussed. An important outcome of the model is that the distribution at full crystallization is determined by the time-dependence of the nucleation and growth rates of grains. In the case under consideration, the theory leads to an analytical expression that has the form of a lognormal-type distribution for the fully crystallized sample.