In order to precisely calculate tangential contact stiffness (TCS) between cylindrical surfaces,this paper presents the establishment of fractal model for TCS calculation between cylinders considering friction factors. This model is obtained by introducing the equation of critical contact area of elastoplastic deformation with friction and employing the basic theory of TCS,based on the fractal contact model of two cylinders’ surfaces,and by employing the Matlab to simulate the model,the changing law of TCS affected by different parameters (such as: friction coefficient,fractal dimension,roughness amplitude,material propertied parameters and curvature radius of cylinders) and contact type is investigated. The numerical results are as follows: the relationship between TCS and normal load is direct ratio,which appears exponential and linear rule respectively with variation of fractal dimension. TCS is inverse proportional to friction coefficient. Effect of material propertied parameters on TCS changes with size of fractal dimension as well as the value itself. The correlations between fractal dimension and TCS,roughness amplitude and TCS are direct or inverse proportion depending on the value of fractal dimension and material propertied parameters. Furthermore,TCS of inner contact is bigger than that of outer contact; TCS increases with curvature radius of cylinders. The theory here helps to analyze the dynamic characteristics between high-pair’s joint surfaces in the future.