Shear friction strength model of concrete was proposed to explain the direct friction mechanism at the concrete interfaces intersecting two structural elements. The model was derived from a mechanism analysis based on the upper-bound theorem of concrete plasticity considering the effect of transverse reinforcement and applied axial loads on the shear strength at concrete interfaces. Concrete was modelled as a rigid–perfectly plastic material obeying modified Coulomb failure criteria. To allow the influence of concrete type and maximum aggregate size on the effectiveness strength of concrete, the stress-strain models proposed by Yang et al. and Hordijk were employed in compression and tension, respectively. From the conversion of these stress-strain models into rigidly perfect materials, the effectiveness factor for compression, ratio of effective tensile strength to compressive strength and angle of concrete friction were then mathematically generalized. The proposed shear friction strength model was compared with 91 push-off specimens compiled from the available literature. Unlike the existing equations or code equations, the proposed model possessed an application of diversity against various parameters. As a result, the mean and standard deviation of the ratios between experiments and predictions using the present model are 0.95 and 0.15, respectively, indicating a better accuracy and less variation than the other equations, regardless of concrete type, the amount of transverse reinforcement, and the magnitude of applied axial stresses.