An approximate method for the analysis of phased arrays of waveguide apertures in a lossy surface is developed. The procedure uses a surface impedance boundary condition in place of modal expansions in the lossy region. The method is validated in the two-dimensional case by comparing numerical results with those obtained by using modal expansions both in the feed waveguide and the lossy medium. The accuracy of the method improves as the magnitude of the lossy dielectric constant increases. The location of the blind spot when the lossy region is backed with a conductor is accurately predicted by the surface impedance method. Calculations of scan dependent matched reflection coefficient, element power gain and power loss to the surface are presented. Salient features of the effects of loss are discussed. The results of the paper permit an extrapolation of the surface impedance method to arrays of realistic waveguide phased array elements with lossy ground.