The use of numerical simulations based on finite element analysis has become essential in designing new products, bridging basic material properties (obtained in various tests performed on material’s specimens) and a product behaviour. Such simulations can account for a real geometry of designed components that can cause stress concentration as well as for in-service loading and/or environmental conditions. A challenging aspect for numerical simulations is anticipating the behaviour of advanced materials such as polymers and composites, demonstrating, i. a., anisotropy, heterogeneity and time-dependent properties as well as non-trivial damage and fracture scenarios. The first step in achieving a valid product simulation is to perform simulations that can accurately reproduce the experimental results. The present work analyzes a possibility to simulate a response of a hyperelastic material (a semi-crystalline thermoplastic polymer) to monotonous uniaxial tensile loadings considering different strain-energy density functions as well as uniaxial cyclic loading using the commercial software ABAQUS/CAE. The former case focuses on a stress–strain curve while the latter one deals with energy hysteresis, strain softening and strain hardening. The performed simulations produce good results for monotonous loading, but simulations of cyclic loading can only partially reproduce the material’s behaviour.