This work presents a wearable device and the algorithms for quantitative modelling of joint spasticity and its application in a pilot group of subjects with different levels of spinal cord injury. The device comprises light-weight instrumented handles to measure the interaction force between the subject and the physical therapist performing the tests, EMG sensors and inertial measurement units to measure muscle activity and joint kinematics. Experimental tests included the passive movement of different body segments, where the spasticity was expected, at different velocities. Tonic stretch reflex thresholds and their velocity modulation factor are computed, as a quantitative index of spasticity, by using the kinematics data at the onset of spasm detected through thresholding the EMG data. This technique was applied to two spinal cord injury subjects. The proposed method allowed the analysis of spasticity at muscle and joint levels. The obtained results are in line with the expert diagnosis and qualitative spasticity characterisation on each individual.