Author Summary This work uses a computational spiking neural network model of physiologically based cortical circuitry to explain the oscillatory responses, known as I-waves, which occur following transcranial magnetic stimulation (TMS) of the motor cortex. The model contains over 38,000 excitatory and inhibitory neurons with 160 million synapses to replicate observed experimental responses to TMS and investigate the structure of population-based circuitry involved in generating coordinated dynamic activity. Abstract Transcranial magnetic stimulation (TMS) is a popular method used to investigate brain function. Stimulation over the motor cortex evokes muscle contractions known as motor evoked potentials (MEPs) and also high-frequency volleys of electrical activity measured in the cervical spinal cord. The physiological mechanisms of these experimentally derived responses remain unclear, but it is thought that the connections between circuits of excitatory and inhibitory neurons play a vital role. Using a spiking neural network model of the motor cortex, we explained the generation of waves of activity, so called ‘I-waves’, following cortical stimulation. The model reproduces a number of experimentally known responses including direction of TMS, increased inhibition, and changes in strength. Using populations of thousands of neurons in a model of cortical circuitry we showed that the cortex generated transient oscillatory responses without any tuning, and that neuron parameters such as refractory period and delays influenced the pattern and timing of those oscillations. By comparing our network with simpler, previously proposed circuits, we explored the contributions of specific connections and found that recurrent inhibitory connections are vital in producing later waves that significantly impact the production of motor evoked potentials in downstream muscles ( Thickbroom, 2011 ). This model builds on previous work to increase our understanding of how complex circuitry of the cortex is involved in the generation of I-waves.