Vulcanizable elastomeric roof sheet materials for roofing having improved burn resistivity and prepared from a polymeric composition of matter comprise 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 non-black 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 or softener per 100 parts of the polymer. A method of covering a roof comprises the steps of applying sheets of vulcanizable elastomeric roof sheet material prepared from a vulcanizable polymeric composition of matter, to the roof being covered; overlapping adjacent edges of the roof sheet material; and adhesively seaming the overlapped layers of the roof sheet material together to form a continuous elastomeric roofing membrane. The composition of matter is devoid of any flame retardant rubber chemical additives, heavy metals and halogen-containing polymers and possess improved burn resistivity.