A shock load isolation mounting system that incorporates a dashpot into each shock load isolation mount to provide damping. Each shock load isolation mount includes a shock mount portion having a first end fixed to the object to be isolated from shock loads, a second end, and an intermediate section between the first end and the second end. Each isolation mount also includes a dashpot mounted in series with the shock mount portion. The dashpot includes a moveable piston and a cylinder that receives the piston therein. The piston is fixed to the second end of the shock mount portion, and the cylinder is fixed to a support that is fixed relative to the object so that the dashpot provides damping in directions parallel to compression and tension directions of the shock mount portion.