Cellular lamellipodia bind to the matrix and probe its rigidity through forces generated by rearward F-actin transport. Cells respond to matrix rigidity by moving toward more rigid matrices using an unknown mechanism. In spreading and migrating cells we find local periodic contractions of lamellipodia that depend on matrix rigidity, fibronectin binding and myosin light chain kinase (MLCK). These contractions leave periodic rows of matrix bound beta3-integrin and paxillin while generating waves of rearward moving actin bound alpha-actinin and MLCK. The period between contractions corresponds to the time for F-actin to move across the lamellipodia. Shortening lamellipodial width by activating cofilin decreased this period proportionally. Increasing lamellipodial width by Rac signaling activation increased this period. We propose that an actin bound, contraction-activated signaling complex is transported locally from the tip to the base of the lamellipodium, activating the next contraction/extension cycle.