Discrete systems are modeled as a network of nodes (particles, molecules, or atoms) linked by nonlinear springs to simulate the action of van der Waals forces. Such systems are nonlocal if links connecting non-adjacent nodes are introduced. For their topological characterization, a nonlocality index (NLI) inspired by network theory is proposed. The mechanical response of 1D and 2D nonlocal discrete systems is predicted according to finite element (FE) simulations based on a nonlinear spring element for large displacements implemented in the FE programme FEAP. Uniaxial force-displacement responses of intact and defective systems (with links or nodes removed) are numerically simulated. Strain localization phenomena, size-scale effects and the ability to tolerate defects are investigated by varying the degree of nonlocality.