The plastic strain localization phenomena are studied with the use of the theory of viscoplasticity and finite element method. The aim of the study is to check if the strain localization is sensitive to variation of initial and boundary conditions. Total and local plastic deformation energy as candidate response functionals for sensitivity analysis are discussed by selected numerical examples of wave propagation problems. The paper considers sensitivity of the form and intensity of plastic strain localization to the variation of the above parameters. Different response functionals for structures demonstrating plastic strain localization were proposed and studied.