Standard theory for liquid infiltration into porous media cannot explain saturation overshoot at an infiltration front. Based on a recent generalization of the Green-Ampt approach, a new theory for variably-saturated flow is presented that assumes that capillary pressure does not only depend on liquid content but also on the flow velocity. The Eulerian expression for the nonequilibrium capillary pressure is rotationally invariant and attempts to capture the conjecture that dynamic effects are more pronounced if flow is associated with moving fluid-fluid interfaces which cause a dynamic contact angle. The new theory correctly predicts how overshoot depends on the downstream and upstream liquid contents as well as on grain size. The theory also yields the hydrostatic pressure distribution in the liquid and allows for liquid contents exceeding the saturated liquid content of the main imbibition curve that may occur for overshoot.