A biaxial stress tester for stressed membranes was constructed by the authors. The tester measures: 1) changes in tension in models of paintings in response to environmental fluctuations; and 2) changes in stiffness (Modulus of Elasticity E ) of the models caused by fluctuations in tension and the environment. Tests performed over a period of eight years showed that the deterioration of surfaces exposed to environmental fluctuations is due to: 1) cycling environmental changes and the resulting stress in these surfaces; and 2) the difference in stiffness between the exposed top surface and its substrate. A surface which is softer than its substrate does not crack. Because the stiffness of stretched canvas fluctuates in response to the environment, it often becomes softer than the paint film that it is supposed to support. This causes the paint film to deteriorate. In addition, overstretching of the canvas during stress-peaks induced by cycling further contributes to the harmful slackening of the canvas support. Numerous practical applications of these findings are given. -- AATA