Abstract: A branch gasket for a tapping sleeve is disposed about the side branch aperture in a main fluid conduit and between and in sealed contact with the main fluid conduit and an outer sleeve connected to the side branch. The branch gasket is comprised of a flexible, compressible, resilient material and includes a hydraulic lip, a stainless steel insert ring, a first pair of inner O-ring seals in intimate contact with the main fluid conduit, and a second pair of outer O-ring seals in intimate contact with the outer sleeve. A mat gasket for use with a tapping saddle is disposed about an aperture in a main fluid conduit and is further disposed between and in sealed contact with the main fluid conduit and an outer sleeve member. The mat gasket includes an aperture aligned with the aperture in the main fluid conduit and outer and inner portions in sealed contact with the outer sleeve member and the main fluid conduit, respectively.