Abstract. The article deals with the problem of creep of a polymer thick-walled cylindrical shell under the action of an uneven temperature field. The calculation is based on the nonlinear Maxwell – Gurevich equation, which is widely used in the calculations of polymer structures. To solve a quasi-stationary nonlinear problem, a "layer-by-layer" method is used, where a layer means a certain time of the process. Such methods for solving creep problems are also called step, sequential loading, incremental, etc. The problem is solved in an axisymmetric formulation under conditions of plane deformation. The use of the Maxwell – Gurevich differential equation allows solving rheology problems when exposed to a timevarying temperature field. The change in the stress state with time and its significant difference from the elastic solution are shown.