This paper is oriented toward the specific testing of polymer composites and textile PA66 cords used as reinforcement for composites. The aim of the research is to validate the proposed new testing methods for low-cyclic testing of polymer composites and PA66 cords for the characterization of material parameters useful as input data for computational tire simulations. Part of the research is the design of experimental methods for polymer composites and test parameters such as load rate, preload, and other parameters such as strain for the start and stop of cycle steps. The DIN 53835-13 standard is used for the conditions of textile cord during the first five cycles. A cyclic load is carried out at two temperatures of 20 °C and 120 °C. The testing method includes a hold step for 60 s between each loop. The video-extensometer technique is used for testing. The paper evaluated the effect of temperatures on the material properties of PA66 cords. The true stress-strain (elongation) dependences between points for the video-extensometer of the fifth cycle of every cycle loop are the data results from composite tests. The forcestrain dependences between points for the video-extensometer are the data results from tests of the PA66 cord. These dependencies can be used as input material data of textile cords in the computational simulation of tire casings using a custom material model definition. The fourth cycle in every cycle loop of polymer composites can be considered a stable cycle because the change in the maximum true stress between the fourth and fifth cycles is 1.6%. Other results of this research include a relationship between stress and the number of cycle loops as the second-degree polynomial curve for polymer composites and a simple relationship to describe the value of the force at each end of the cycles for a textile cord.