The statistical behavior of linear chains confined in a thin slab is investigated theoretically as a model of polymer-mediated adhesion. We apply transition-matrix methods to two lattice models of the polymer: model A consists of end-grafted monodisperse polymer chains, model B of randomly grafted infinitely long chains. We evaluate both the elongational and the tangential moduli, the first being generally larger than the latter. We also derive by a Flory-Huggins approach the contribution to the elongational modulus of the polymer compressibility or of a swelling solvent. (C) 2003 American Institute of Physics.