Finite-element methods are used to study non-adhesive, frictionless rough contact of elastic and plastic solids. Roughness on the contact surfaces is realized by self-affine fractal. True contact area between spherical rough surfaces and flat rigid surfaces rises in power law as the external normal load increases. The power exponent is sensitive to surface roughness as well as the curvature of spherical geometry. Surface contact pressures are analyzed and compared for elastic and plastic solids. The distribution of local contact pressure is significantly dependent on the surface roughness and the yield stress of plastic solids.