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Biomedical applications of near infrared radiation (NIR) techniques (i.e., based on light wavelengths roughly between 400 and 1100 nm) require that a preliminary estimate of the tissue volume being investigated be found. One possible estimate is the depth to which a photon penetrates a tissue before it eventually emerges at a separating plane at a given time. A simple model for this problem can be based on a lattice random walk and was initially analyzed when the associated optical coefficients are isotropic with respect to the geometry. Here we include the effects of anisotropy in the optical coefficients, finding that at long times the statistical properties of the depth of penetration can be accounted for by very simple scaling factors while at short times the anisotropy factors can be quite significant.