The problem of the mechanical behavior is formulated for flexible metal-reinforced composite plates in conditions of steady creeping of all phases of the materials composition. The equations, describing with varying degrees of accuracy the stress-strain state in such plates with account of their weakened resistance to the transverse shears, are obtained. The equations of the classical Kirkhoff theory, of non-classical Reissner theory and of the second variant of Timoshenko theory are appeared as special cases of these equations. The linearization of the equations is carried out on base of the method of secant modulus. For axially loaded and axially reinforced annular plates with clamped one edge and statically loaded on another edge, the simplified variant of the improved theory was developed, for which the complexity of practical realizing is comparable with the complexity of Reissner theory. Specific calculations are carried out for the bending deformation of and axially reinforced annular plates at different levels of heat loadings. It is shown that with increasing temperature the accuracy of the calculations in the framework of the traditional theories is reduced and they do not provide even 20% accuracy of determining the flexibility of such structures. It is found that the reinforcement in the directions of the main averaged stress and strain rate is not always rational from the point of view of reducing the flexibility plates in conditions of steady creep. It is shown that the traditional theory of classical and nonclassical can lead to the wrong solution of problems of optimal and rational design of flexible reinforced thin-walled structural elements.