We use contact dynamic simulations to perform a systematic investigation of the effects of particles shape angularity on mechanicals response in sheared granular ma-terials. The particles are irregular polyhedra with varying numbers of face from spheres to "double pyramid" shape with a constant aspect ratio. We study the quasi-static behav-ior, structural and force anisotropies of several packings subjected to triaxial compression. An interesting finding is that the shear strength first increases with angularity up to a maximum value and then saturates as the particles become more angular. Analyzing the anisotropies induced by the angular distributions of contacts and forces orientations, we show that the saturation of the shear strength at higher angularities is a consequence of fall-off of the texture anisotropies compensated by an increase of the tangential force anisotropy. This is attributed to the fact that at higher angularity, particles are bet-ter connected (or surrounded) leading to an increase of friction mobilization in order to achieve the deformation. Moreover, the most angular particles also have very few sides so that, this effect is enhanced by the increase of the proportion of face-side and side-side contacts with angularity.