The tensile viscoelastic responses of live, innervated rabbit skeletal muscle were measured and characterized using the quasi-linear model of viscoelasticity. The tibialis anterior (TA) and extensor digitorum longus (EDL) muscles of anesthetized New Zealand white rabbits were surgically exposed and tested under in vivo conditions. Rate sensitivity of the force-time history was observed in response to constant velocity testing at rates from 0.01 to 2.0 Hz. Average hysteresis energy, expressed as a percentage of maximum stored strain energy, was 39.3 ± 5.4% and was insensitive to deformation rate. The quasi-linear model, with constants derived from relaxation testing, was able to describe and predict these responses with correlation exceeding the 99% confidence interval for the 132 constant velocity tests performed (r_mean = 0.9263 ± 0.0373). The predictive ability of this model was improved when compressive loading effects on the muscle were neglected, r_mean = 0.9306 ± 0.0324. The rate insensitivity of hysteresis energy was predicted by the model;​ however, the absolute value of the hysteresis was underestimated (30.2 ± 4.0%). Both muscles demonstrated strikingly different elastic functions. Geometric normalization of these responses (stress and strain) did not result in a single elastic function capable of describing both muscles. Based on these results, the quasi-linear model is recommended for the characterization of the structural responses of muscle;​ however, further investigation is required to determine the influence of muscle geometry and fiber architecture on the elastic function.