Flat rubber sheets are joined together at their primed surfaces utilizing an adhesive tape composition which features at least one EPDM rubber and will provide a long-term, water-tight barrier. The adhesive tape composition is a solventless, preformed, tacky composition comprising a) at least one crosslinkable EPDM rubber, b) a filler, either of the reinforcing or semi-reinforcing variety, c) one or more compatible tackifiers, d) a softener, and lastly, e) a cure system for the rubbery polymer. The tape composition itself has excellent ozone, moisture, weathering and heat aging resistance as well as superior low temperature properties.