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Whisker flick stimulation is a commonly used protocol to investigate somatosensory processing in rodents. Neural activity evoked by whisker flicks produces a characteristic electroencephalography (EEG) waveform known as a somatosensory evoked potential. In this paper, we use computational modeling to make predictions about the neural populations that contribute to this signal, either through their own membrane currents or the membrane currents they elicit in downstream populations. While the model cannot fully explain the mechanisms of somatosensory evoked potential (SEP) generation, we predict that the initial positive deflection of the EEG waveform is driven largely by direct thalamic inputs to layer 2/3 and layer 5 pyramidal cells, while the negative deflection is driven by a more complex mix of sources, including thalamic and recurrent cortical connectivity. Small changes to the local connectivity of the circuit can have an important impact on the recorded EEG, without substantially affecting firing rates, suggesting that EEG may be useful in constraining in silico neural models.