We have developed a new geomechanical workflow to study the mechanics of hydraulic fracturing in naturally fractured unconventional reservoirs. This workflow used the material point method (MPM) for computational mechanics and an equivalent fracture model derived from continuous fracture modeling to represent natural fractures (NFs). We first used the workflow to test the effect of different stress anisotropies on the propagation path of a single NF intersected by a hydraulic fracture. In these elementary studies, increasing the stress anisotropy was found to decrease the curving of a propagating NF, and this could be used to explain the observed trends in the microseismic data. The workflow was applied to Marcellus and Eagle Ford wells, where multiple geomechanical results were validated with microseismic data and tracer tests. Application of the workflow to a Marcellus well provides a strain field that correlates well with microseismicity, and a maximum energy release rate, or integral at each completion stage, which appeared to correlate to the production log and could be used to quantify the impact of skipping the completion stages. On the first of two Eagle Ford wells considered, the MPM workflow provided a horizontal differential stress map that showed significant variability imparted by NFs perturbing the regional stress field. Additionally, a map of the strain distribution after stimulating the well showed the same features as the interpreted microseismic data: three distinct regions of microseismic character, supported by tracer tests and explained by the MPM differential stress map. Finally, the workflow was able to estimate, in the second well with no microseismic data, its main performance characteristics as validated by tracer tests. The field-validated MPM geomechanical workflow is a powerful tool for completion optimization in the presence of NFs, which affect in multiple ways the final outcome of hydraulic fracturing.