There is a growing need to develop accurate nonlinear viscoelastic material models and tools that could describe the complex nonlinear behavior of being developed composite material systems at their simulations at high loads and temperatures or to move the industry towards more sustainable bio-based alternatives. Developing such models in 3D formulation for materials with changing material state due to physical aging, change of crystallinity or degree of cure is also imperative since the loading is mostly multiaxial in real-live applications and manufacturing processes. The present paper contains the derivation of two material models with varying complexity and accuracy. The incremental procedure for implementation of the nonlinear viscoelastic material model within the numerical analysis was presented. Two relatively simple simulations with the incremental methodology developed were performed, namely triaxial mechanical loading and thermal stress development during the manufacturing process. The results obtained showed significant differences between stresses calculated using 1D and 3D simulations. Significantly higher stresses obtained in 3D simulations demonstrated the necessity of 3D models.