Motile cells moving in vitro do so via a characteristic motile appendage, the lamellipod, a broad, flat region of the cell cytoplasm which extends ahead of the moving cell, and which is devoid of organelles. I describe here a mechanochemical model for how the lamellipod propels the cell forward. The propulsive force for the spreading of the lamella derives from the swelling pressure of the cytogel within the lamellipod. A local change in ionic conditions - caused by a leak through the leading membrane - activates solating factors, which upsets the equilibrium between the gel osmotic pressure and its elasticity. Subsequently, regelling and contraction pull the cell forward. The model is in accordance with a diverse array of experimental observations on cell motility, and suggests a common physical mechanism underlying a variety of cell motility phenomena.