Magneto- and/or electro-encephalography (M/EEG) are non-invasive clinically-relevant tools that have long been used to measure electromagnetic fields in somatosensory cortex evoked by non-painful and painful somatosensory stimuli. Two commonly applied stimulation paradigms that produce distinct responses in primary somatosensory cortex (SI) linked to non-painful and painful sensations are electrical median nerve (MN) stimulation and cutaneous laser-evoked (LE) stimulation to the dorsum of the hand, respectively. Despite their prevalence, the physiological mechanisms that produce stereotypic macroscale MN and LE responses have yet to be fully articulated, limiting their utility in understanding brain dynamics associated with non-painful or painful somatosensation. We examined the neocortical circuit mechanisms contributing to MN and LE responses in SI using the Human Neocortical Neurosolver (HNN) neural modeling software tool. HNN was specifically designed for biophysically principled interpretation of the cell and circuit origin of M/EEG signals (Neymotin et al., 2020). Detailed analysis of the timing and orientation of peaks in source localized SI current dipole responses from MN and laser-evoked (LE) stimulation showed that these features were robust and conserved across prior studies. The first peak in the MN response at ~20 ms corresponds to outward-directed deep-to-superficial electrical current flow through the cortical laminae, while the initial LE response occurs later at ~170 ms and is oriented in the opposite direction. Historically, these peaks have both been labeled N20 and N1, despite their opposite current orientations. Simulating the cellular and circuit-level mechanisms accounting for these and later peaks with HNN's detailed laminar neocortical column model revealed that the MN response can be simulated with a sequence of layer-specific exogenous excitatory feedforward and feedback synaptic drive. This sequence was similar to that previously reported for tactile evoked responses (Jones et al., 2007; Neymotin et al., 2020), with the novel discovery of an early excitatory feedback input to superficial layers at ~30 ms post-stimulus that facilitated generation of the MN response's first prominent inward-oriented deflection, known historically as the P30. Simulations of the LE response revealed that the initial ~170 ms inward-deflection required a burst of repetitive gamma-frequency (~40 Hz) excitatory supragranular feedback drives, consistent with prior reports of LE gamma-frequency activity. These results make novel and detailed multiscale predictions about the dynamic laminar circuit mechanisms underlying temporal and spectral features of MN and LE responses in SI, and can guide further investigations in follow-up studies. Ultimately, these findings may help with the development of targeted therapeutics for pathological somatosensation, such as chronic and neuropathic pain.