Layer IV of rodent somatosensory cortex contains identifiable networks of neurons, called “barrels,” that are related one-to-one to individual whiskers on the face. A previous study (Simons and Carvell, 1989) described differences between the response properties of thalamic and cortical vibrissa neurons and proposed that these transformations can be explained by several features of barrel anatomy and physiology: nonlinear neuronal properties, strongly responsive inhibitory and less responsive excitatory neurons, convergent thalamic inputs to cells of both types, and interconnections among barrel neurons. In the present study these features were incorporated into a computational model in order to test their explanatory power quantitatively. The relative numbers of excitatory and inhibitory cells and the relative numbers of synapses of thalamic and intrabarrel origin were chosen to be consistent with available light and electron microscopic data. Known functional differences between excitatory and inhibitory barrel neurons were simulated through differences in spike activation functions, refractory periods, postsynaptic potential decay rates, and synaptic strengths. The model network was activated by spike trains recorded previously from thalamic neurons in response to three different whisker deflection protocols, and output, which consisted of spikes generated by the simulated neurons, was compared to data from our previous neurophysiological experiments. For each type of whisker stimulus, the same set of parameter values yielded accurate simulations of the cortical response. Realistic output was obtained under conditions where each barrel cell integrated excitatory and inhibitory synaptic inputs from a number of thalamic and other barrel neurons and where the ratios between network excitation, network inhibition, and thalamic excitation were approximately constant. Several quantities are defined that may be generally useful in characterizing neuronal networks. One important implication of the results is that thalamic relay neurons not only provide essential drive to the cortex but could, by changing their tonic activities, also directly regulate the tonic inhibition present in the cortex and thereby modulate cortical receptive field properties.