Abstract: In a diaphragm device, a round diaphragm of flexible material comprising a rim clamped between and sealingly gasketing upper and lower housing members, a coaxial annular arched vault within and circumferentially continuously joined at its outer periphery to the rim and having an inner downwardly directed periphery connected to an obliquely downwardly-facing disk-shaped portion including a molded-in or otherwise incorporated shape-maintaining oblique core disk to afford an integral swingable shiftable portion useful as a valving member in a shutoff type actuated valve or a check valve, or as the operably shiftable main part of a pump diaphragm, for which examples are disclosed.