In the present study, a coupled 3D transient Eulerian thermo-chemical analysis together with a 2D plane strain Lagrangian mechanical analysis of the pultrusion process, which has not been considered until now, is carried out. The development of the process induced residual stresses and strains together with the distortions are predicted during the pultrusion in which the cure hardening instantaneous linear elastic (CHILE) approach is implemented. At the end of the process, tension stresses prevail for the inner region of the composite since the curing rate is higher here as compared to the outer regions where compression stresses are obtained. The separation between the heating die and the part due to shrinkage is also investigated using a mechanical contact formulation at the die-part interface. The proposed approach is found to be efficient and fast for the calculation of the residual stresses and distortions together with the temperature and the cure distributions.