In this paper we analyze the possibility of extending the photothermal methods developed for thermal diffusivity measurements of isotropic materials [A. Salazar and A. Sánchez-Lavega, Rev. Sci. Instrum. 65, 2896 (1994)] to the case of anisotropic specimens. A full theoretical treatment of the photothermal signal generation for the case of an anisotropic sample with its principal axes aligned with the sample surface is presented. Three photothermal detection schemes have been studied: infrared radiometry, photothermal reflectance, and optical beam deflection (mirage effect). The fundamental result we have obtained is that when using infrared radiometry, photothermal reflectance and collinear mirage setups, the thermal magnitude retrieved is the resistivity to heat diffusion (a tensor defined as the inverse of the thermal diffusivity tensor). Only the perpendicular mirage experiment allows one to directly retrieve the thermal diffusivity along any direction of the material. Experimental measurements performed on two highly anisotropic materials confirm the above-mentioned results.