S U M M A R YWe present the extension of stereotomography to P-and S-wave velocity estimation from PP-and PS-reflected/diffracted waves. In this new context, we greatly benefit from the use of locally coherent events by stereotomography. In particular, when applied to S-wave velocity estimation from PS-data, no pairing of PP-and PS-events is a priori required. In our procedure the P-wave velocity model is obtained first using stereotomography on PP-arrivals. Then the S-wave velocity model is obtained using PS-stereotomography on PS-arrivals fixing the Pwave velocity model. We present an application to an 'ideal' synthetic data set demonstrating the relevance of the approach, which allows us to recover depth consistent P-and S-waves velocity models even if no pairing of PP-and PS-events is introduced. Finally, results to a real data set from the Gulf of Mexico are presented demonstrating the potential of the method in a noisy data context.