A modified casing coupling houses a pressure relief valve body having a through bore with opposing end openings. The through bore communicates with the interior of the modified casing coupling at one end opening thereof and with an area surrounding the modified casing coupling at an opposite end opening. The through bore includes a ball seat adjacent one end opening thereof which receives a sealing ball. The ball is urged in the direction of the ball seat by a tensioning element. The ball is exposed to annular pressure trapped between successive lengths of well casing located in the well borehole. The amount of tension exerted on the ball by the tensioning element is selected to allow the ball to move off the ball seat to release trapped annular pressure between the selected casing strings once a certain annulus pressure is reached.