Different quantitative ultrasound techniques are currently developed for clinical assessment of human bone status. This paper is dedicated to axial transmission: emitter(s) and receiver(s) are linearly arranged on the same side of the skeletal site, preferentially the forearm, a referenced site to predict fracture risk in case of osteoporosis. In several clinical studies, the signal velocity of the earliest temporal event has been shown to discriminate osteoporotic patients from healthy subjects. However, a multi parameter approach might be relevant to improve bone diagnosis and this be could achieved by accurate measurement of guided waves phase velocities. Clinical requirements and bone/soft tissue heterogeneities constrain the length probe to about 10 mm. Thus efficiency of conventional spatio-temporal Fourier transform is reduced. Efficiency of time-frequency techniques was shown to be moderate in other studies. Signal processing to obtain reliable guided wave velocities is a key point. A technique, taking benefit of using both multiple emitters and multiple receivers, is proposed. The guided mode phase velocities are obtained using a projection in the singular vectors basis. Those are determined by the singular values decomposition of the transmission matrix between the two arrays at fixed frequencies. This method was first validated on metallic plates, enabling us to recover accurately guided waves phase velocities for moderately large array. A set of excised human bone samples (radius) were then probed. Attention was paid to observation of cut-off frequencies because of their high power of discrimination of relevant properties (thickness, elasticity) for bone characterization. The analysis of the whole spectrum, including several branches of intermediate phase velocities is under progress. The so-called bi-directional correction of the soft tissue thickness variations under the probe is used for the in vivo measurements. Therefore a mode classification of the raw data was developed, together with a calibration of the probe.