The deformation of a glassy amorphous polymer has been simulated by Monte Carlo. A molecular model with constrained chemical bonds (rigid‐bond model) and one with chemical bonds represented by Gaussian springs (flexible‐bond model) have been compared. Furthermore, two different deformation protocols have been tested. Comparisons on the basis of stress–strain behavior, contributions of various interactions to stress and energy, evolution of density and distribution of dihedral angles, and of pair correlation functions show that both the introduction of constrained bonds and the deformation protocol influence the results dramatically. The results obtained using the flexible‐bond model, employing a deformation protocol in which all the monomers are displaced affinely with the box size, show the best agreement with experimental facts.