We present a simple model which illustrates the nature of the contact between an elastic solid and a hard surface with cosine-corrugation profile. In the continuum limit, the contact mechanics depends only on two dimensionless parameters, namely the ratio between the height and wavelength of the substrate corrugation, and the ratio between a surface energy and an elastic energy. The theory shows that the complete contact state is always a local energy minima (in the zero temperature limit), but for large enough surface roughness the global minima correspond to a partial contact state. We show that at nonzero temperature, the contribution to the free energy from the vibrational entropy is very important, and favors the detached state. Computer simulations results are also presented where we study more complicated roughness geometries and the influence of temperature on the adhesion. Simulation results agrees well with the analytical predictions. (C) 2003 American Institute of Physics.