The group velocity of the S0 mode of a Lamb wave under the first cut-off frequency is measured during the tensile loading for the unidirectional composite materials. The group velocity of the S0 mode has the characteristic of increasing with the strain. The propagation velocity of a wave is generally proportional to the square root of the ratio of the modulus to the density. The elastic modulus is considered as a constant as the stress linearly increases with the strain. The increase of the group velocity with the strain is caused by a decrease in the density. It is proposed that the measurement of the group velocity of the S0 mode is useful for making an evaluation of the tensile strain and of any degradation in the unidirectional composite materials.