There are provided an acrylate polymer elastomer containing a particular acrylic ester unit as a constitutive component, and a vulcanizable composition comprising the elastomer and a vulcanizing agent.The acrylate polymer elastomer is obtained by copolymerizing(a) 45 to 89.9 wt. % of a monomer represented a by the formula ##STR1## wherein R.sup.1 represents an alkyl group having 1 to 8 carbon atoms, and/or a monomer represented by the formula ##STR2## wherein R.sup.2 represents an alkylene group having 1 to 8 carbon atoms and R.sup.3 represents an alkyl group having 1 to 8 carbon atoms,(b) 10 to 35 wt. % of a monomer represented by the formula t,0012 wherein R.sup.4 represents a hydrogen atom or a methyl group, R.sup.5 represents a hydrogen atom or a hydrocarbon group having 1 to 4 carbon atoms, and n represents an integer of 1 to 5,(c) 0.1 to 10 wt. % of crosslinkable monomer, and(d) 0 to 30 wt. % of a monoethylenic unsaturated monomer copolymerizable with the above(a) , (b) and (c) components.A vulcanizate obtained from the vulcanizable composition has improved low temperature resistance and oil resistance and is excellent in the balance of both natures.