The analysis of the stability and strength criterion of reinforced concrete shells during deformation according to the harmonic law under the action of axial compression is carried out. A method for determining the criterion of durability of reinforced concrete according to the momentless theory is presented. Options for estimating the stress-strain state of shells at a constant and variable modulus of elasticity are considered. An analogy is given between the behavior of quantities in the semi-momentless and momentless theories of zero-curvature shells. A method for calculating reinforced concrete structures of coatings under conditions of rheological deformation is presented, reflecting their real work, as well as taking into account the random nature of the values taken in the calculation. © The Authors, published by EDP Sciences.