Method and apparatus for leak testing a closed container with at least one flexible wall area, whether or not the container undergoing leakage testing is is filled with a product or not. A biasing member is moved towards and onto the flexible wall area in order to apply a predetermined force and the accompanying reaction forces are monitored over time. The instant invention of this leakage or integrity testing system constitutes an improvement over conventional prior art pressure monitoring sytems by instead monitoring a biasing force applied by such biasing member to such flexible wall area at different times over a testing cycle, whereby storage of two biasing force values at different times allows the later processing of a difference signal that is generated by using two measured force signals over time to thus result in both a leak indicative signal and an updated compensating zero offset signal. Furthermore, the moving of the biasing member may be done at a constant rate or predetermined rate, or the moving accomplished by establishing a pressure difference between the inside of the container and its ambient surroundings, such as may be done by evacuating such surroundings by application of vacuum.