The stress-strain state of the polymer ring is analyzed in this paper. The analytical methods were used to calculate the viscoelastic displacements of the ring: method based on the solution of the three-dimensional equations of the visco -elasticity; method connected with the nonlinear equations of the hereditary theory and method based on the solution of the space contact problem of the visco-elasticity. The comparative results are given on the displacements for all of the analytic methods. The comparison of the linear and nonlinear approaches to the solution of the problem and advices on the choice of the most suitable polymer, which has the least deformations, is given.
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