Golf balls having improved cut and shear resistance that include covers and/or other layers formed from polyurea compositions formed with at least one amine-terminated polytetramethylene ether glycol homopolymer, at least one amine-terminated copolymer of polytetramethylene ether glycol and polyalkylene glycol. The amine-terminated polytetramethylene ether glycol homopolymer or amine-terminated copolymer of polytetramethylene ether glycol and polyalkylene glycol may be used as the isocyanate-reactive in the prepolymer and/or the curing agent.