Rats rhythmically sweep their whiskers over object features, generating sequential deflections of whisker arcs. Such moving wavefronts of whisker deflection are likely to be fundamental elements of natural somatosensory input. To determine how moving wavefronts are represented in somatosensory cortex (S1), we measured single- and multiunit neural responses in S1 of anesthetized rats to moving wavefronts applied via a piezoelectric whisker deflector array. Wavefronts consisted of sequential deflections of individual whisker arcs, which moved progressively across the whisker array. Starting position (starting arc), direction, and velocity of wavefronts were varied. Neurons responded strongly only when wavefront starting position included their principal whisker (PW). When wavefronts started at neighboring positions and swept through the PW, responses to the PW arc were suppressed by up to 95%, and responses over the entire wavefront duration were suppressed by up to 60% compared to wavefronts that initiated with the PW. Suppression occurred with inter-arc deflection delays of ≥5 ms, was maximal at 20 ms, and recovered within 100-200 ms. Suppression of PW arc responses during wavefronts was largely independent of wavefront direction. However, layer 2/3 neurons showed direction-selectivity for responses to the entire wavefront (the entire sequence of SW and PW arc deflection). Wavefront direction selectivity was correlated with receptive field somatotopy, and reflected differential responses to the specific SWs that were deflected first in a wavefront. These results indicate that suppressive inter-whisker interactions shape responses to wavefronts, resulting in increased salience of wavefront starting position, and, in some neurons, preference for wavefront direction.