A new model is developed that considers the effect of roughness on the elastic contact of spherical bodies. A general pressure distribution is proposed that encompasses the contact of rough spheres and yields the Hertzian theory for ideally smooth surfaces. A new parameter, nondimensional maximum contact pressure, is introduced and it is shown that this is the key parameter that controls the contact. The results of the present study are presented in the form of compact relationships. These relationships are compared against the experimental data collected by others and good agreement is observed.