This paper presents an ultrasonic measurement technique to determine an elasticity parameter, called the apparent compliance, in a thin-walled tube. The apparent compliance is obtained by ultrasound pulse-echo measurement of the diameter variation in response to an externally applied time-varying pressure function. Specifically, the diameter variation is obtained by tracking the time shift of the echoes from the front and back walls of the tube using a correlation technique. This technique is named the Forced Vibration Method (FVM). This approach to compliance measurement is distinctly different from compliance measurements using the blood function as excitation function, but is closely related to the elastic imaging concept. Two experimental models, termed the rigid wall model and the leg-like model, have been developed. These models allow the amplitude and frequency of the pressure function as well as the dimensions and properties of the tube to be varied. Results for the diameter variations vs. location along the tube and frequency of external pressure function are presented for both models.