P receiver functions (PRFs) and the H-k stacking technique are tools often used to constrain the thickness of the crust and the ratio between the velocities of P and S waves. Both the crustal depth and the Poisson's ratio are very important parameters to study the tectonic evolution of the lithosphere, but they can be significantly affected by the presence of crustal anisotropy. In order to address this problem, we have extended the isotropic stacking approach to include six converted P-to-S phases that are generated in the anisotropic case, instead of only three phases considered in the isotropic case, and we have examined the feasibility of the stacking technique using synthetic and real data. Based on PRFs acquired by 108 permanent broadband seismic stations deployed in the southeastern margin of Tibet including the Sichuan and Yunnan areas, we have applied the anisotropic H-k stacking scheme to investigate the crustal thickness and Poisson’s ratio. The results reveal that the crustal thickness varies from ∼60 km in the Songpan-Ganzi fold system and the northern part of the Sichuan-Yunnan diamond-shaped block, near the Eastern Himalayan Syntaxis, to ∼33 km in southern Yunnan, and that the Poisson’s ratio varies mostly from 0.24 to 0.32. The highest values of 0.28–0.30 are found along the axis formed by the Longmenshan fault, the Lijiang-Jinhe fault and the Xiaojiang fault, and are attributed to the accumulation of lower crustal flow in front of the Sichuan Basin. The highest value of ∼0.32 is observed at the Tengchong volcano area to the north of the Indochina block, and is attributed to the upwelling of hot mantle associated to the eastward subduction of the Indian plate, rather than to the expansion of east Tibet. Comparing with the results provided by the isotropic stacking scheme, it is appreciated that the crustal depth determined by the anisotropic stacking method well adjusts the observed pattern of gravity anomaly. We conclude that the results obtained by anisotropic stacking yield a much better constraint on the estimation of the crustal depth and Poisson's ratio when compared to those achieved by isotropic stacking.