Case's method of normal mode expansion is applied to the slab albedo problem, i.e., the problem of finding the angular density in a bare slab with neutrons incident upon one face. The problem is reduced to determining expansion coefficients which are shown to depend upon the solution of two nonhomogeneous Fredholm integral equations. Using Neumann iteration to solve for the coefficients, we obtain explicit solutions for the angular density, scalar density, and net current in zeroth- and first-order approximations.