Bladder dysfunction is a major health risk for people with spinal cord injury. Recently, we have demonstrated that epidural sacral spinal cord stimulation (SCS) can be used to activate lower urinary tract nerves and provide both major components of bladder control: voiding and continence. To effectively control these functions, it is necessary to selectively recruit the afferents of the pudendal nerve that evoke these distinct bladder reflexes. Translation of this innovation to clinical practice requires an understanding of optimal electrode placements and stimulation parameters to guide surgical practice and therapy design. Computational modeling is an important tool to address many of these experimentally intractable stimulation optimization questions. Here, we built a realistic MRI-based finite element computational model of the feline sacral spinal cord which included realistic axon trajectories in the dorsal and ventral roots. We coupled the model with biophysical simulations of membrane dynamics of afferent and efferent axons that project to the lower urinary tract through the pelvic and pudendal nerves. We simulated the electromagnetic fields arising from stimulation through SCS electrodes and calculated the expected recruitment of pelvic and pudendal fibers. We found that SCS can selectively recruit pudendal afferents, in agreement with our experimental data in cats. Our results suggest that SCS is a promising technology to improve bladder function after spinal cord injury, and computational modeling unlocks the potential for highly optimized, selective stimulation. Clinical Relevance - This model provides a method to non-invasively establish electrode placement and stimulation parameters for improving bladder function with epidural spinal cord stimulation.