The preceding chapters of this book address computational challenges inherent to elastoplastic models at the local (material point) level and present tailored numerical solutions. However, at the structural scale, simulations employing constitutive models with softening laws for failure analysis encounter severe mesh dependency due to the loss of ellipticity in governing partial differential equations following strain localization. To preserve mesh objectivity, regularization methods that introduce a material’s intrinsic characteristic length are essential. Among these, the integral nonlocal method stands out for its computational efficiency, as it avoids modifying PDEs or introducing additional degrees of freedom. In this chapter, we first revisit the foundational principles of nonlocal integration methods. Building on this, we propose a novel nonlocal implicit stress update algorithm that synergizes the LSM with integral nonlocal regularization, specifically applied to a non-orthogonal Mohr-Coulomb damage model. For plastic computations, nonlinear stress integral equations are resolved via the line search technique, while damage computations employ nonlocal averaging of the strain-softening variable to regularize structural-level finite element solutions. Furthermore, a consistent tangent operator is derived using complex step derivative approximation, ensuring quadratic convergence in global equilibrium iterations. The efficacy of the algorithm is rigorously evaluated through five boundary value problems, demonstrating its robustness in structural failure analysis.