To provide a single cylinder hydraulic shock absorber capable of exhibiting necessary and sufficient damping force even during the compression stroke, and capable of improving riding comfort in a vehicle.

This vehicular single cylinder hydraulic shock absorber D1 is provided with a cylinder 1, a free piston 2 slidably inserted into the cylinder 1 and partitioning an inside of the cylinder 1 to a liquid chamber L and a gas chamber G, a piston 3 slidably inserted into the cylinder 1 and partitioning the liquid chamber L to two pressure chambers R1 and R2, and a rod 4 having an end connected to the piston 3. An elastic member S energizing the free piston 2 toward the liquid chamber L is disposed in the gas chamber so that the spring constant is increased when compression is advanced.