Based on contact fractal theory, a modified MB fractal model, and from the energy dissipation point and considering the mechanism of energy dissipation of joint interfaces, tangential damping and its dissipation factor models of joint interfaces are proposed. Numerical simulations reveal the varying relations of tangential damping and its dissipation factor versus corresponding parameters such as fractal dimension, fractal roughness, friction factor, and plastic index. A micro convex nonlinear relation (when fractal dimension is between 1.1 and 1.4) or near linear relation(when fractal dimension is between 1.4 and 1.9) between dimensionless tangential damping and dimensionless normal contact force over the joint interfaces varies with the fractal dimension of the surface profiles, dimensionless tangential damping increases(when fractal dimension is between 1.1 and 1.7) or decreases (when fractal dimension is between 1.7 and 1.9) with the increment of fractal dimension, and decreases with the increase of dimensionless fractal roughness. While the influences of plastic index, the ratio of hardness to yield strength, and the ratio of total tangential force to total normal force on dimensionless tangential damping are similar, and a concave nonlinear relation between tangential damping dissipation factor and the normal contact force over the joint interfaces, the tangential damping dissipation factor, meanwhile, decreases with the increment of the friction factor. In addition, the validation of the tangential contact damping model is implemented in indirect ways, which make comparison between the proposed tangential stiffness model and the literature.