Inverse problems of the theory of elasticity for inhomogeneous bodies, as a rule, are used to identify the dependence of the mechanical properties of the material from the coordinates. It is known that in a thick-walled cylindrical or spherical shell under internal or external pressure the highest stresses are occurred close to the internal surface of the shell. The article presents several solutions of inverse problems, which are defined dependence of the elastic modulus of the radius, at which the equivalent stress in the shell is constant. Corresponding shells can be called equal stress shells. In most cases the change of the module of elasticity of a material leads to changes in its strength. It is shown that for some materials it is possible to create model of equal strength shell in which equivalent stress in each point is equal to material strength. In the article is also considered the way of modification material's deformation properties at which beams and rods, working under combined stress state (for example, the eccentric compression of columns, the strip foundation and so forth), are also will be equal stress. © 2016 The Authors.