A stabilizer is provided for stabilizing a rotary or progressive cavity pump suspended from production tubing in well casing. The stabilizer is connected between the production tubing and the pump. The stabilizer has a tubular body having a cylindrical wall and a longitudinal bore contiguous with the production tubing. A releasable sliding dog is disposed on the exterior of the tubular body and is operatively connected by a link to one or more pistons. Each piston is disposed in a piston housing that is in fluid communication with the bore of the tubular body. Circumferentially spaced-apart feet extend radially outwardly from the tubular body. In operation, actuating fluid pressure advances the pistons uphole, driving the sliding dog up one or more longitudinal outwardly extending ramps to brace against the casing, with the feet contacting the casing and bearing opposing reactive force. Preferably, the sliding dog and the feet form a three-point contact with the casing that arrests lateral movement in any direction. Under non-actuating pressure, upward drag on the sliding dog compresses the pistons, retracting the dog, and permitting removal of the stabilizer and pump.