In this article, we present a general solution for the ac temperature field of an opaque material containing aligned subsurface cylinders produced by a modulated line illumination parallel to the cylinders. This work completes the case of plane illumination treated in a previous paper [J. M. Terrón, A. Salazar, and A. Sánchez-Lavega, J. Appl. Phys. 91, 1087 (2002)]. The model includes the multiple scattering effects suffered by the cylindrical thermal wave, generated by the line heat source, when interacting with the cylinders and with the sample surfaces. Numerical calculations illustrate the effect of buried cylinders on the sample surface temperature. This model is then used to calculate the in-plane effective thermal diffusivity of unidirectionally fiber-reinforced composites. We also calculate the decrease of this effective thermal diffusivity as a consequence of the presence of a thermal resistance between fibers and matrix. Experimental measurements using modulated photothermal techniques on calibrated samples confirm the validity of the results.