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This paper is dedicated to modeling deformation and fractureprocesses whose localization and development are restricted to some part ofthe surface of a structural element and are caused either by pronounced localthermomechanical effects (problem A) or by a local corrosion damage of thepart (problem B). Within the problem A the model for describingdeformation and fracture of the material of a plate subjected, on a part of itssurface, to thermomechanical action is considered. Within the problem Bthe model for describing deformation and fracture of the cylinder withcorrosion zone subjected to thermomechanical action is considered. In bothcases the thermal action applied to the surface is determined by atemperature jump on one of its sides, whereas the other side is heatinsulated. The mechanical action is due to stresses applied to one side of thedeformed part of the surface.