The shear plasticity of charge density waves (CDW) in NbSe3 single crystals with cross sections having a single microfabricated thickness step was investigated. Thickness-dependent CDW pinning was found to be responsible for the origin of shear stresses along the step. The CDW depinned elastically at the volume average depinning field for small thickness differences, whereas the weak pinned side depinned first through plastic shear, for large thickness differences. Shear plasticity contributed substantial dissipation above the depinning field in large thickness differences. Shear strength of approximetaely 9.5 × 103 Nm-2 was indicated by a model that described the qualitative features of CDW.