An analytical approach for the adhesion of a semi-infinite elastic body in contact with a sinusoidal rigid surface under zero external pressure is presented. Although Johnson (Int. J. Solids Struct. 32, 423 (1995)) has proposed an analytical solution for a slightly wavy surface, while Zilberman and Persson (Solid State Commun. 123, 173 (2002); J. Chem. Phys. 118, 6473 (2003)) have given a numerical solution for a highly wavy surface by considering the curvature of the contact area in the calculation of the interfacial term of the total energy, our solution is not only for small amplitude of roughness (i.e., the slightly wavy surface as Johnson's) but also for large amplitude of roughness (i.e., the highly wavy surface as of Zilberman and Persson). Our solution considers the curvature of the contact area as do Zilberman and Persson. Our results which are obtained for the total energy and equilibrium condition of the system agree with both Johnson's and Zilberman and Persson's results. The effects of the material constants and the surface roughness on the adhesion are clearly expressed and discussed.