A thermomechanical model based on physical representations of the motion of dislocation continuum and a model for the initiation and propagation of plastic shear are proposed to describe slow flows of the type of Luders bands. Two-dimensional calculations of Luders band propagation are performed for HSLA-65 steel samples under compression at various strain rates and temperatures. The calculation results are in good agreement with experimental data.Introduction. Constructing physicomechanical models of homogeneous deformation that describe the mechanical behavior of metals and alloys at various rates and temperatures is an important problem of modern mechanics. From a physical point of view, it is also necessary to develop approaches to modeling inhomogeneous flows. Substantially inhomogeneous deformation is exemplified by the propagation of Chernov-Luders localized plastic deformation bands. In experiments, a Luders band is usually observed as a macroscopic zone of localized plastic deformation, which forms near the base macroscopic stress concentrator (as a rule, near the tensile grip) and propagates throughout the sample at a rate characteristic of the particular grade of steel.The goal of the work is to construct a combined model for the mechanical behavior of metals that includes a relaxation equation taking into account the rate and temperature sensitivity and describes the initiation and propagation of localized plastic deformation bands.General System of Equations and Initial and Boundary Conditions. To describe material deformation, we use the system of equations including the laws of conservation of mass and momentum, strain relations, and the constitutive equations describing the material. The mechanical behavior of the examined steel grade is modeled for a plane strain state. A numerical solution is constructed in Lagrangian variables using a finite difference method [1,2].In the case of plane strain, the following strain rate tensor components are nonzero: