Abstract: The stress analytical solution for plane problem of a thick-walled cylinder subjected to a type of non-uniform distributed pressures is given by the complex variable function method. The results show that tangential stresses and/or radial stresses change into tensile stresses from compressive stresses with the increase of non-uniform lateral pressure coefficient. And the value of tangential tensile stress is much larger than that of radial tensile stress. On the premise of non-existence of tensile stress zones, the range of non-uniform lateral pressure coefficients is back-calculated and the tensile stress zones corresponding to different non-uniform lateral pressure coefficients are given. Theoretical analysis results are verified by numerical method.