The paper presents the results of experimental studies and mathematical modeling of the effect of stress accumulation in thermosetting epoxy polymer "hot" curing on anhydride hardener. Stress accumulation occurs under cyclic thermomechanical action in a locked rod, similar effects are observed, for example, in thermoplastic elements subjected to the combined effect of mechanical loads and variable temperatures. Experimental results have shown that under cyclic thermomechanical loading during exploitation it is possible to accumulate residual stresses in the thermosetting polymer. A multi-element structural mathematical model with memory for thermomechanical load, which allows to consider the accumulation of residual thermal stresses, has been proposed. The results of modeling and experiment are compared. Based on the results, corrections are made in the approach to the application of this model to thermosetting polymers such as the epoxy resin under study. Considering the corrections, a good agreement (the difference is from 1 to 6%) with the results of experimental determination of stresses under complex cyclic thermomechanical load was obtained.