Elastomeric polymers, such as polyurethane (PU), are being used in novel applications to enhance the load-carrying capacity, ductility, and the survivability of structures under dynamic loading. The mechanical response of elastomeric materials is highly rate and pressure dependent, and exhibits stress-strain non-linearity. The objective of the current study is to identify the effect of the strain rate on the uniaxial tensile behavior of elastomeric PU. To this end, four types of PUs differing in their plasticizer content were used. The uniaxial tensile characteristics under loading and unloading conditions and the cyclic softening behavior were examined under varying strain rate regimes (ranging from 0.001 s⁻¹ to 0.33 s⁻¹). The experimental results showed that the stress-strain behavior of all PUs is non-linear and rate dependent. Young’s module, yield stress, tangent module, ultimate tensile stress, failure stress, failure strain, resilience module, toughness module and residual strain of PU6 at 0.33 s⁻¹ are 0.37–4.13 times compared to the values at 0.001 s⁻¹. It also exhibits hysteresis and cyclic softening. Increasing strain rates resulted in a dramatic transition in behavior from rubbery to leathery for all PUs. This behavior was described as positive strain-rate dependence. The behavior of PUs was defined as hyper-viscoelastic material.