Pain-related sensory input is processed in the spinal dorsal horn (SDH) before being relayed to the brain. That processing profoundly influences whether stimuli are correctly or incorrectly perceived as painful. Significant advances have been made in identifying the types of excitatory and inhibitory neurons that comprise the SDH, and there is some information about how neuron types are connected, but it remains unclear how the overall circuit processes sensory input or how that processing is disrupted under chronic pain conditions. To explore SDH function, we developed a computational model of the circuit that is tightly constrained by experimental data. Our model comprises conductance-based neuron models that reproduce the characteristic firing patterns of spinal neurons. Excitatory and inhibitory neuron populations, defined by their expression of genetic markers, spiking pattern, or morphology, were synaptically connected according to available qualitative data. Using a genetic algorithm, synaptic weights were tuned to reproduce projection neuron firing rates (model output) based on primary afferent firing rates (model input) across a range of mechanical stimulus intensities. Disparate synaptic weight combinations could produce equivalent circuit function, revealing degeneracy that may underlie heterogeneous responses of different circuits to perturbations or pathologic insults. To validate our model, we verified that it responded to the reduction of inhibition (i.e., disinhibition) and ablation of specific neuron types in a manner consistent with experiments. Thus validated, our model offers a valuable resource for interpreting experimental results and testing hypotheses in silico to plan experiments for examining normal and pathologic SDH circuit function.