We present a numerical procedure for elastic and nonlinear analysis (including fracture situations) of solid materials and structures using the discrete element method. It can be applied to strongly cohesive frictional materials such as concrete and rocks. The method consists on defining nonlocal constitutive equations at the contact interfaces between discrete particles using the information provided by the stress tensor over the neighbor particles. The method can be used with different yield surfaces, and in the paper, it is applied to the analysis of fracture of concrete samples. Good comparison with experimental results is obtained.