This paper develops a methodology for investigating the stress–strain state and evaluating the load-bearing capacity of metal plates strengthened by plasma electrolytic oxidation of the surface layer. The object of analysis is a plate of symmetric structure with a double-side oxide coating subjected to biaxial tensile loading under uniform heating and in the presence of a self-equilibrated field of residual stresses. Within the framework of the plane-sections’ and elastic-deformation hypothesis, the closed-form analytical expressions are obtained for the residual stresses in the substrate and in the oxide layers in terms of the incompatible strain of the surface layers, as well as for the total stress state under combined thermomechanical loading. Two strength criteria are formulated and analysed: a global (integral) criterion, which is insensitive to self-equilibrated residual and thermal components, and a local criterion, which reduces to a set of linear inequalities for the admissible load and temperature at a given level of residual stresses. The capabilities of the methodology are illustrated by computational examples for the Al/Al₂O₃ (6061-T6 alloy/aluminium oxide) and Ti/TiO₂ (Grade 2 titanium/titanium dioxide) compositions, with account of the Pilling–Bedworth ratio and the mismatch of linear thermal-expansion coefficients of the metal and its oxide. As shown, in the absence of thermal effects and residual stresses, the load-bearing capacity of an oxidized plate in tension is about three times lower than that of the uncoated plate, owing to high stress concentration in the thin stiff coating. The combinations of residual-stresses’ level and temperatures are identified, at which an oxidized plate operates as an equal-strength structure with maximum load-bearing capacity; explicit analytical relations are obtained for both the Al/Al₂O₃ and Ti/TiO₂ systems.