Near-threshold tactile stimuli perception and somatosensory temporal discrimination threshold (STDT) are encoded in the primary somatosensory cortex (S1) and largely depend on alpha and beta S1 rhythm. Transcranial alternating current stimulation (tACS) is a non-invasive neurophysiological technique that allows cortical rhythm modulation. We investigated the effects of tACS delivered over S1 at alpha, beta, and gamma frequencies on near-threshold tactile stimuli perception and STDT, as well as phase-dependent tACS effects on near-threshold tactile stimuli perception in healthy subjects. In separate sessions, we tested the effects of different tACS montages, and tACS at the individualised S1 μ-alpha frequency peak, on STDT and near-threshold tactile stimuli perception. We found that tACS applied over S1 at alpha, beta, and gamma frequencies did not modify STDT or near-threshold tactile stimuli perception. Moreover, we did not detect effects of tACS phase or montage. Finally, tACS did not modify near-threshold tactile stimuli perception and STDT even when delivered at the individualised μ-alpha frequency peak. Our study showed that tACS does not alter near-threshold tactile stimuli or STDT, possibly due to the inability of tACS to activate deep S1 layers. Future investigations may clarify tACS effects over S1 in patients with focal dystonia, whose pathophysiology implicates increased STDT.