This article describes computational simulations of tensile tests of polymeric composites with the determination of material parameters. Composites consist of an elastomeric rubber matrix and textile or steel cords as reinforcement. Stress–strain analyses are performed. The ANSYS APDL (ANSYS Parametric Design Language) procedure is used to create computational models simply and quickly. Single- and two-layer models are created for simulations. A two-parameter Mooney–Rivlin material model is used for the rubber matrix. Comparisons are made with experimental data attention is paid to comparing the data with the video-extensometer. Therefore, the tests are called basic tensile tests if the dependence of tensile force–displacement between gauges is measured, but if the video-extensometer is used, the outputs from tests are dependencies between true stress and true strain in the work area of specimens. Tests with video-extensometer are called specific tests. The dependence of true strain–transverse strain for the two-layer specimen is done as a control curve to verify that the video-extensometer correctly measured the deformations at the measuring points. The data obtained from tests are tensile strength, ductility, contraction, Poisson's ratio, and tensile modulus of elasticity. The computational models take this into account. The difference between the computational simulation results and the experimental data is approximately 10%.