Electrical stimulation of the pudendal nerve (PN) is a promising approach to restore continence and micturition following bladder dysfunction resulting from neurological disease or injury. Although the pudendo-vesical reflex and its physiological properties are well established, there is limited understanding of the specific neural mechanisms that mediate this reflex. We sought to develop a computational model of the spinal neural network that governs the reflex bladder response to PN stimulation. We implemented and validated a neural network architecture based on previous neuroanatomical and electrophysiological studies. Using synaptically-connected integrate and fire model neurons, we created a network model with realistic spiking behavior. The model produced expected sacral parasympathetic nucleus (SPN) neuron firing rates from prescribed neural inputs and predicted bladder activation and inhibition with different frequencies of pudendal afferent stimulation. In addition, the model matched experimental results from previous studies of temporal patterns of pudendal afferent stimulation and selective pharmacological blockade of inhibitory neurons. The frequency- and pattern-dependent effects of pudendal afferent stimulation were determined by changes in firing rate of spinal interneurons, suggesting that neural network interactions at the lumbosacral level can mediate the bladder response to different frequencies or temporal patterns of pudendal afferent stimulation. Further, the anatomical structure of excitatory and inhibitory interneurons in the network model was necessary and sufficient to reproduce the critical features of the pudendo-vesical reflex, and this model may prove useful to guide development of novel, more effective electrical stimulation techniques for bladder control.