An adhesive tape composition includes a polymer blend comprising at least one EPDM rubber, and preferably three EPDM rubbers in substantially equal amounts, and an adhesive-enhancing polymer selected from the group consisting of polyisoprene, polybutadiene, and ethylene-propylene copolymer and mixtures thereof. The tape adhesive composition further includes at least one tackifying additive compatible with said polymer blend and a sulfur and organic accelerator cure package for said polymer blend, the adhesive composition being devoid of butyl rubber which is found in most other adhesive tape compositions. This composition is seen as providing excellent long-term heat aging, weathering resistance, and low temperature properties as compared to adhesive tape compositions containing butyl rubber. Moreover, the adhesive tape composition provides more surface tack, better "quick-grab", and higher green strength as compared to adhesive tape compositions containing 100 percent EPDM rubber. A method is also provided for covering roofs which includes the step of employing the adhesive tape composition.