The thermal viscoplastic stresses and the dislocation densities in silicon ribbon are computed for an axially changing thermal profile by using an iterative finite difference method. A material constitutive equation (Haasen–Sumino model) which involves an internal variable (mobile dislocation density) is used. The results are interpreted as showing that there is a maximum width of silicon ribbon that can be grown when viscoplasticity and dislocations are considered. This maximum width limitation does not exist if the material behavior is elastic.