The resolving equations were obtained and a calculation technique was developed with allowance for the nonlinear creep of three-layer plates and shallow shells with a lightweight filler. The problem was reduced to a system of three differential equations with respect to the stress function, displacement and deflection function. An example is given of calculating a rectangular planar shell in the form of an elliptical paraboloid. The solution was performed numerically by the finite difference method in combination with the Euler method for determining creep strains. The linear Maxwell-Thompson equation and the Maxwell-Gurevich nonlinear equation were used as the creep law. There were no significant discrepancies between the results obtained on the basis of the linear and nonlinear theory. It was established that, as the curvature of the shell increases, the creep of the aggregate has a lesser effect on the deflection value. It was revealed that for shells of greater curvature with constant displacements a redistribution of stresses and internal forces occurs. The bending and twisting moments decrease, and the longitudinal and shearing forces increase. In the aggregate, the tangential stresses relax, while in the sheaths the normal and tangential stresses increase.