Vulcanizable elastomeric roof sheet materials for roofing having improved adhesion performance and prepared from a polymeric composition of matter comprising at least one polymer selected from the group consisting of polyolefins prepared from monomers containing at least two carbon atoms and mixtures thereof, the polymer having a crystallinity of up to about 2 percent by weight; about 20 to 125 parts by weight of one or more mineral fillers per 100 parts of the polymer, about 50 to 110 parts by weight of one or more black-type fillers per 100 parts of the polymer; and from about 50 to 70 parts by weight of a processing material per 100 parts of the polymer and having improved peel adhesion to itself using commercially available bonding and lap- splice adhesives. A method of covering a roof comprises the steps of applying layers of vulcanizable elastomeric roof sheet material prepared from a vulcanizable polymeric composition of matter, to the roof being covered; overlapping adjacent edges of the layers; and adhesively seaming the overlapped edges of the layers together to form an acceptable seam. The composition of matter is devoid of any flame retardant rubber chemical additives, heavy metals, oxidants and halogen-containing polymers.