It is known that human can feel the vibratory envelope on periodic sinusoidal vibrations; however, the role of the envelope on non-periodic transient vibrations is still not clear. This study investigated Just Noticeable Difference (JND) of the time constant in the decaying sinusoidal vibration model, which is one reasonable factor relating to discrimination of tapped materials. The authors conducted psychophysical experiments to evaluate JNDs for two referenced time constants (10.8 and 50 ms) among five frequencies (150, 250, 500, 800 and 1000 Hz). The analysis showed that significant frequency effect on JNDs was only found for the lower JNDs of reference time constant 50 ms. JNDs of the time constant was lower around 250 Hz (150 to 500 Hz, average JND was 12.8%) and was higher at high frequencies (800 to 1000 Hz, average JND was 27.9%). No significant frequency effects were found in the upper JNDs of reference 50 ms (average JND was 23%) and upper JNDs of reference 10.8 ms (average JND was 65%).