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The microstructural evolution of multicrystalline silicon ribbons produced by the RGS process (Ribbon Growth on Substrate) is analysed by numerical simulation. The crystallization model takes into account the facetted growth structure of silicon, thermal supercooling in front of the crystallization front and nucleation dependent on the thermal supercooling. The thermal conditions for the crystallization of the ribbon are taken from a macroscopic finite element simulation of the RGS process, as it is realized at Bayer AG, Germany. Different crystallization morphologies - single crystal, columnar multicrystal or dendritic - are discussed in their dependence on the process and nucleation conditions. The numerical results are compared to morphologies of silicon ribbons, grown on the pilot plant of Bayer AG, Germany.