Samples of poly(etherether ketone) (PEEK) were subjected to large plastic deformations under uniaxial tension and simple shear by means of a new video-controlled testing method at constant true strain rate. The "equivalent" stress-strain curves obtained under the two loading modes are close at the yield point, but diverge drastically at large strains, with a rapidly increasing hardening in tension and a moderate hardening under simple shear. X-ray diffraction goniometry shows that these contrasting behaviors are associated with the different textures developed in the crystallite orientations. Under tension, the PEEK lamellae are progressively tilted in such a way that the chain axis becomes oriented parallel to the tensile axis; in the other mode, the final chain orientation is near to the shear axis. DSC analyses of deformed samples in both modes are carried out. The results show that the tension loading induces a fragmentation of the thin lamellae, while the shear mode generates less fragmentation. A quantitative model is presented that involves a composite approach : i) the viscoplastic deformation of the crystalline lamellae, which is controlled by chain slip and transverse slip systems on planes parallel to the c axis, and ii) the hyperelastic deformation of the amorphous phase, which depends on the affine unfolding of statistically distributed subchains. A discussion of the influence of the CRSS values on the stress-strain curves and textures is developed by means of this model.