Abstract: A twin tube shock absorber having inner and outer tube with an annular reservoir between the tubes. A piston in the inner tube divides the inner tube into an upper chamber and a lower chamber and valves through the piston control stiffness of the shock absorber. An acceleration sensitive valve assembly mounted in the base valve makes the shock absorber “soft” upon downward acceleration of the wheel of the vehicle in which the shock absorber is mounted. The valve assembly includes a port for fluid communication between the lower chamber and a conduit, and an inertial mass blocking the port in a port-closed position and not blocking the port in a port-open position. The inertial mass is normally in a lower port-closed position in absence of downward acceleration of the tubes of the shock absorber. Upon downward acceleration of the tubes, the inertial mass moves upwardly toward a port-open position where fluid flow through the port is not blocked.