Plane strain thermomechanical deformations of a viscoplastic body are studied with the objective of analyzing the localization of deformation into narrow bands of intense straining. Two different loadings, namely, the top and bottom surfaces subjected to a prescribed tangential velocity, and these two surfaces subjected to a preassigned normal velocity, are considered. In each case a material defect, flaw, or inhomogeneity is modeled by introducing a temperature bump at the center of the specimen. The solution of the initial boundary value problem by the Galerkin-Adams method reveals that the deformation eventually localizes into a narrow band aligned along the direction of the maximum shearing strain. For both problems, bands of intense shearing appear to diffuse out from the center of the specimen.