A shock absorber apparatus includes a rod; a tool connection on a first end of the rod; a piston on a second end of the rod; a flange on the rod between the tool connection and the piston; a ring connection slidably connected to the rod between the tool connection and the flange; a first spring between the ring connection and the flange to bias the ring connection axially away from the flange; a sleeve, connected to a second spring between the second spring and the piston, slidably encircling the piston and a portion of the rod, and extending past the piston to a pumpdown connection; and a fin. A method for a placing a tool in a landing ring of a drilling tubular includes using the shock absorber apparatus to absorb shocks caused by the landing operation.