The internal structure of concrete is a three-phase material, namely matrix, aggregate, and the interface between them. Concrete, as a widely used material in engineering, its macroscopic mechanical properties and fracture characteristics are crucial for structural safety. Crack propagation is mainly caused by stress concentration near the crack tip, and T-stress, as a constant term stress near the crack tip, plays a decisive role in the crack propagation path. In this paper, the stress intensity factors of cracks near aggregate are calculated by analytical numerical method. Firstly, the contact interface between aggregate and matrix is defined as the spring layer contact interface, and then the analytical continuation method is used. Finally, an approximate analytical solution for the influence of circular aggregates on the stress intensity factor at the crack tip is obtained by calculation. The result show that the cohesive material and T-stress can influence the fracture toughness and the crack tip stress. This provided the basis for simulation of concrete fracture.