Abstract: The anisotropic Yb∶KGW laser crystal may have the zero thermal lens effect in some propagation directions, according to the measurement results of Biswal et al and Pujol et al. The thermal expansion tensors of Yb∶KGW crystals mentioned in these two references were obtained by least square and tensor rotation methods respectively. And the athermal directions were calculated on the basis of the thermal expansion tensors. The comparison and analysis show that, although there is some difference between individual crystals, this kind of crystals generally has only two athermal directions instead of four athermal directions calculated by Biswal et al, that is to say, the angles between these two athermal directions and p axis are around ±20° in the p-g plane when light is polarized in m direction. Besides, the calculated thermo-optic properties in certain directions with thermal expansion tensor taken into account are consistent with the laser thermal lensing experimental results reported by Swedish Hellstrom et al.