Contact of rough surfaces is a very important and practical engineering problem.The normal contact stiffness of rough surfaces in elastic state was studied by Hertz elastic theory and random contact model of rough surface.The normal contact stiffness formulae in different contact bodies were derived.The conclusion can be drawn from theoretical formula that the normal contact stiffness is proportional with the load,and inversely proportional to the mean square value of the surface roughness,in the random contact model of rough surfaces.