A sealing arrangement for a pump includes a first member having a peripheral wedge-shaped pocket; a second member with a rim opposed to the pocket; and a diaphragm disposed between the two members. The diaphragm includes a central stem, a disk-shaped head attached to the stem, and an upstanding bead disposed around the periphery of the head. The bead includes a first angled surface and a second angled surface. The bead is received in the pocket so as to form two separate, spaced-apart sealing surfaces between the diaphragm and the first member. The sealing arrangement may also include a gasket made from a resilient material and having a flat web with a circular crosssection bead disposed in a gland between two members. The dimensions of the bead and the gland are selected such that the bead is diametrically compressed at least about 40% from its free state.