Mechanical and viscoelastic properties of precision polyolefins, poly(4-phenylcyclopentene) (P4PCP) and its hydrogenated analog (H2-P4PCP) containing atactic phenyl branches at exactly every five carbons along the backbone are explored. Both materials are amorphous with a glass transition temperature of ∼17 ± 3 °C. Rheological investigations determined that P4PCP has an entanglement molar mass (Me = 10.0 kg mol–1) much higher and closer to polystyrene than H2-P4PCP (Me = 3.6 kg mol–1). Both materials have elastomeric and shape memory properties at ambient temperatures, which were further explored through strain hysteresis measurements. H2-P4PCP has an elastic recovery of ∼95% at max strain values up to 500% as determined by uniaxial tensile testing. Time–temperature superposition analysis, Williams–Landel–Ferry constants, and further mechanical analysis are discussed and compared to previously reported ethylene–styrene copolymers of similar phenyl-branch content within the microstructure.