Issues of feasibility and stability are considered for a finite horizon formulation of receding horizon control for linear systems under mixed linear state and control constraints. We prove that given any compact set of initial conditions that is feasible for the infinite horizon problem, there exists a finite horizon length above which a receding horizon policy will provide both feasibility and stability, even when no end or stability constraint is imposed. Finally, computations for determining a sufficient horizon length are carried out on a simple open-loop stable example under control saturation constraints.