The associative analogue of the integral equation theory developed by Madden and Glandt is applied to a model of methane adsorbed in a silica xerogel. The integral equations are solved in the associative Percus-Yevick approximation. The associative treatment of strong attraction between fluid particles and matrix species in this model yields a better description of the pair distribution functions at intermediate fluid densities and at low temperatures in comparison with the Percus-Yevick approximation. In contrast to the Percus-Yevick approximation, the associative Percus-Yevick theory gives solutions for some subcritical temperatures of the bulk fluid. The adlayer structure is discussed in terms of the fraction of bonded species and coordination numbers. The behavior of the distribution functions and internal energy coincides with the Monte Carlo simulation data of Kaminsky and Monson. It is shown that the model can be used for the description of different Lennard-Jones fluids in hard sphere matrices. Possible refinements of the theory by using the replica Ornstein-Zernike equations of Given and Stell are discussed briefly.