The process induced variations such as residual stresses and distortions are a critical issue in pultrusion, since they affect the structural behavior as well as the mechanical properties and geometrical precision of the final product. In order to capture and investigate these variations, a mechanical analysis should be performed. In the present work, the two dimensional (2D) quasi-static plane strain mechanical model for the pultrusion of a thick square profile developed by the authors is further improved using generalized plane strain elements. In addition to that, a more advanced 3D thermo-chemical-mechanical analysis is carried out using 3D quadratic elements which is a novel application for the numerical modelling of the pultrusion process. It is found that the 2D mechanical models give relatively reasonable and accurate stress and displacement evolutions in the transverse direction as compared to the 3D model. Moreover, the generalized plane strain model predicts the longitudinal process induced stresses more similar to the ones calculated in the 3D model as compared with the plane strain model.