We performed simulations and experiments of wavefront distortions induced by propagating through diode-pumped square-section amplifying laser rods of Nd-doped phosphate glass and 0.5%Nd:5%Lu:CaF2. We observed that depending on the material, wavefront distortions' profile can vary from a circular lens-like distortion to a complex astigmatic distortion. We showed that this difference comes from the relative sign of piezo-optic tensor coefficients.