The development of highly transparent solids for fiber optics, integrated optics, and high power lasers requires improved methods to measure very low absorption coefficients. For the case in which a laser beam, modulated at angular frequency omega, passes through a weakly absorbing solid which is surrounded by a confined, nonabsorbing gas, the temperature profiles in the solid and the temperature and pressure profiles in the gas have been calculated. The calculations suggest that for sufficiently low frequencies and high ambient gas pressures, enough heat transfers from the solid to the gas to produce a detectable acoustic-pressure signal at angular frequency omega in the gas. They also indicate that an absorbing layer at the solid-gas interface is not an essential mechanism for producing these detectable acoustic pressure signals. The model assumes that bulk absorption in the solid is the mechanism by which energy is transferred from the laser beam. Numerical examples for a typical laser glass are given.