Abstract <p>In the existing studies, the solution of the axisymmetric deformation problem of the circular membrane under the action of non-uniformly distributed loads is obtained by using the small-rotation-angle assumption, which makes the application of the existing research results have great limitations. In order to provide an analytical solution with a wider application range and higher accuracy, this paper abandons the small-rotation-angle assumption and re-establishes the mathematical model of prestressed circular membrane under non-uniformly distributed loads, and provides its analytical solution. Through static equilibrium analysis, the out-of-plane equilibrium equation is established and the small-rotation-angle assumption commonly used in existing studies is discarded. And then, the governing equations and boundary conditions are presented by the elastic mechanics and an axisymmetric problems of planar radial stretching. The analytical solution of the studied problem is given by using the power series method. The validity and application scope of the obtained solutions are analyzed by comparing with existing studies. Based on the specific numerical examples, the effects of the small-rotation-angle assumption, the load change coefficient and initial stress on the deflection deformation of circular membranes are analyzed. The results show that the solution obtained here applicable to the case of both small and large rotation angles. Furthermore, the computational error of the small-rotation-angle assumption decreases with the increase of initial stress.</p>