Abstract: A flexible, water impervious shell is shaped to fit over a portion of a person's arm or leg that is secured in a cast and to extend beyond the cast. The shell has a closed end that is shaped to fit over the extremity of the arm or leg, and an open end opposite thereto. When the shell is tightly secured to the skin of the arm or leg at the open end, a pressure seal is created between the shell and the skin at the open end of the shell. An inflation valve communicating through the shell enables the air pressure inside the shell when the shell is fitted over the arm or leg and the open end is tightly secured to the skin, to be increased to thereby reinforce the pressure seal. The exterior surface of the water impervious material of the shell is covered with a fabric, such as nylon, for providing resistance to slippage when the exterior of the cover is wet, except that the exterior region of the water impervious material of the shell near the open end is not covered by fabric.