Muscle tissue is prone to changes in composition and architecture following stroke. Changes in muscle tissue of the extremities are thought to increase resistance to muscle elongation or joint torque under passive conditions. These effects likely compound neuromuscular impairments, exacerbating movement function. Unfortunately, conventional rehabilitation is devoid of precise measures and relies on subjective assessments of passive joint torques. Shear wave ultrasound elastography, a tool to measure muscle mechanical properties, may be readily available for use in the rehabilitation setting as a precise measure, albeit at the muscle-tissue level. To support this postulation, we evaluated the criterion validity of shear wave ultrasound elastography of the biceps brachii; we investigated its relationship with a laboratory-based criterion measure for quantifying elbow joint torque in individuals with moderate to severe chronic stroke. Additionally, we evaluated construct validity, with the specific sub-type of hypothesis testing of known groups, by testing the difference between arms. Measurements were performed under passive conditions at seven positions spanning the arc of elbow joint flexion-extension in both arms of nine individuals with hemiparetic stroke. Surface electromyography was utilized for threshold-based confirmation of muscle quiescence. A moderate relationship between the shear wave velocity and elbow joint torque was identified, and both metrics were greater in the paretic arm. Data supports the progression toward a clinical application of shear wave ultrasound elastography in evaluating altered muscle mechanical properties in stroke, while acknowledging that undetectable muscle activation or hypertonicity may contribute to the measurement. Shear wave ultrasound elastography may augment the conventional method of manually testing joint mobility by providing a high-resolution precise value. Tissue-level measurement may also assist in identifying new therapeutic targets for patient-specific impairment-based interventions.