Investigated is the propagation of localized plastic deformation fronts in a material with boride coating. Dynamic boundary-value problem is solved in the plane-strain formulation. Numerical simulation is performed by the finite-difference method. Microstructure of the composite is taken into account explicitly in calculations and corresponds to those experimentally observed. Constitutive equations for the steel substrate include an elastic-plastic model with isotropic strain hardening taking into account a relation to describe slow flows. Deformation and fracture of the coated material under external compression is shown to be controlled by the appearance of local regions of tension along the interface. An interaction and interplay between nonhomogeneous plastic deformation in the steel substrate and crack origination and growth in the coating are studied. Cracking patterns, location of the fracture onset and volume fraction of failed material are found out to depend on the velocity of Lьders front propagation.