The extended Hertzian analysis is investigated of elastic and elasto-plastic contact between sphere and rough surfaces. The theoretical analysis is presented using simplified rough surface models for estimating the effects on normal approach in variation of the parameters such as relatively topographical features and material constants in constitutives (sphere and flat plane with asperities). It is assumed that the asperity consists of a part of the sphere, the uniform stress is applied at the bottom of the asperity, and that horizontal displacements of each asperity are neglected. The asperities in the range of 21 × 21 squares are incrementally indented by the spheres. The normal, Gausian, distributions are applied to both heights and intervals of the asperities being on the flat plane. It was found that in elastic contact the present results, including the effects of the parameters, of the normal approach vs. load diagrams obtained here lied in between the Hertzian and the Greenwood analysis. No appreciable qualitative differences, however, should be found between elastic and elasto-plastic contacts.