A two-dimensional computer model is presented to study the development of microstructure and crystallographic texture in polycrystalline films growing on amorphous substrates, which often exhibit strong textures. In particular, the analysis focuses on the influence of growth parameters such as the crystal habit, the relative growth rate along different crystal directions, the nucleation density on the substrate surface and the substrate topography. The simulation explains the development of fiber and in-plane textures in polycrystalline films growing from randomly oriented nuclei. These textures result from a geometric selection of the orientation of crystals, mainly due to differences in growth rates along different crystal directions. The calculated distribution of crystal orientations and its evolution with time are In agreement with textures observed in films deposited under growth conditions, corresponding to zone 2 of the structure zone model. The growth of crystals composing of a polycrystalline film is mainly constrained by the growth of adjacent crystals and the geometry of the environment where crystal growth takes place. For instance, average lateral crystal size scales with time as a power law, the exponent varying as a function of the curvature and/or topography of the substrate.