The article presents results of research of a damper with passive and semi-active damping using polymer springs (also artificial muscles or nylon springs) with negative thermal expansion. Passive damping can be ensured by the strong damping effects of polymer springs. Semi-active damping can be provided by heating the springs from an additional heat source. According to design such dampers, mathematical models for analytical thermoelastostatic analyzes of dampers for selected load cases are processed in the paper. The permissible values ​​of mechanical and thermal load of the dampers are determined. The results obtained are verified by numerical analysis using the finite element method. The elastostatics of the passive damper was verified on a real model of the damper. The compiled mathematical models can be used in the design of polymer dampers as well as in their automatic control. Designed and analyzed dampers can be used in smaller mobile or stationary systems such as scooters, small car kits and the like.