Pulse wave velocity (PWV) is widely used for estimating the stiffness of an artery. However, PWV is an average indicator of artery stiffness between two measuring points, and therefore does not identify local stiffness. We have developed a noninvasive method for generating and detecting the wave propagation in the arterial wall. The phase velocity can be measured accurately over a few millimeters. In this paper, a mathematical model for group velocity analysis is developed from a three-dimensional cylindrical shell theory. Experimental studies on group velocity are carried out on natural latex tubes in air. The theoretical analysis agrees with the experiments well. The theory can be used for estimating the elasticity of arteries from the group velocity measurements.