Adhesion is attractive and has a close relation to many modern problems of contacts between plastically deformable surfaces on the micro/nano-scale (such as microelectromechanical systems (MEMS) and nanotechnology). In the present paper a theoretical model is developed to obtain a better understanding of the adhesion of rough surfaces with plastic deformation. The present research goes beyond the Gaussian and exponential distributions of microasperity heights by introducing the description of self-affine fractal surfaces. General expressions for real contact area, total load and required separation force are derived. Two new dimensionless parameters are derived, which are used in further analysis of adhesion together with the existing roughness exponent and plastic adhesion index, giving a quantitative understanding about adhesion with plastic deformation and the relevant phenomenon.