Spasticity after a stroke is usually assessed in a score form by subjectively determining the resistance of a joint to an externally imposed passive movement. This work presents a spasticity measurement system for on-line quantifying the stretch reflex of paretic limbs. Four different constant stretch velocities in a ramp-and-hold mode are used to elicit the stretch reflex of the elbow joint in spastic subjects. The subjects are tested at supine position with the upper limb stretched towards the ground, in contrast with the horizontally stretched movement used in other studies. By subtracting the baseline torque, reflex torque measured at a selected low stretch velocity of 5 deg/sec, the influence of gravity torque and inertial in vertical stretching mode can be minimized. The averaged speed-dependent reflex torque (ASRT), defined as the measured torque deviated from the baseline torque, is used for quantifying the spastic hypertonia. Four subjects having incurred cerebrovascular accident (CVA) are recruited for time-course study in which the measurements are taken at 72 hours, one week, one month, three months, and six months after onset of stroke. During the development of spasticity, the changes of ASRT and velocity sensitivity of ASRT of the involved and the intact elbow joints are discussed.