In the present paper, the authors regard fiber reinforced composite materials as macroscopical homogeneous orthotropic body. By means of Christoffel's equation of plane wave, the relationship formulas between the phase velocities of plane wave and the elastic constants are determined. If the phase velocities are measured with the help of the experimental method, the elastic constants can be obtained by the formulas. Based on this principle, the elastic constants are determined with the experimental method for four kinds of materials. They are: steel, GRP laminate, GRP lamina and carbon fiber-epoxy lamina. A comparison is made between the experimental method and the resonance method. Finally the characteristics of the phase velocity method are dealt with briefly and some proposals to improve the experiment are also suggested.