Particle shape has a significant effect on the microscopic and macroscopic mechanical behavior of granular assemblies. This paper focuses on effects of particle angularity on the mechanical behavior of granular materials and evolution of the contact force anisotropy during direct shear tests. To this end, a discrete polyhedral element model with a general contact force law for arbitrarily shaped bodies is carried out. Particle angularity is defined in terms of the sphericity and the number of vertexes of a polyhedron. Four groups of assemblies with different particle angularities consist of non-cohesive mono-sized reasonably symmetric polyhedral particles. Direct shear tests are simulated using a modified version of the open source DEM code YADE. The results show that: the granular assembly has increasing shear strength and dilatation as particle angularity increases; the effect of angularity on the shear strength and dilative behavior of assemblies is more significant as the vertical loading is larger; the anisotropy of normal contact force increases at the start, then decreasing to remain a relatively stable value during shearing; and a larger change of the anisotropy of normal contact force after shearing is corresponding to a larger angularity.