The main objective of the present paper is the numerical investigation of dynamic shear bands in inelastic solids during impact--loaded adiabatic processes. An idea of this investigation has been inspired by recent experimental observations performed by Guduru, Rosakis and Ravichandran, {\it Mechanics of Materials} {\bf 33} (2001), 371--402. Their experimental work has brought deep understanding of the initiation and propagation characteristics as well as temperature field evolution of dynamic shear bands in C~300 maraging steel. A photograph of an arrested shear band in the specimen showed that the thickness of the band is about 40~$\mu$m (so it is mesoscale size range). Utilizing the finite element method and ABAQUS system for regularized thermo--elasto--vis\-co\-plas\-tic constitutive model the numerical investigation of dynamic shear band propagation in an asymmetrically impact--loaded prenotched plate is presented. We idealize the initial boundary value problem investigated experimentally by assuming the velocity boundary condition and different material of the specimen (HY--100 steel). Shear band advance, shear band velocity and the development of the temperature field as a function of time have been determined. Qualitative comparison of numerical results with experimental observation data has been presented.