The periodically distributed fracture spacing phenomenon exists in the failure process of the reinforced concrete prism under uniaxial tension. In this paper, A numerical code RFPA3D (3D Realistic Failure Process Analysis) is used to simulate the three-dimensional failure process of plain concrete prism specimen and reinforced concrete prism specimen under uniaxial tension. The reinforced concrete is represented by a set of elements with same size and different mechanical properties. They are uniform cubic elements and their mechanical properties, including elastic modulus and peak strength, are distributed through the specimens according to a certain statistical distribution. The elastic modulus and other mechanical properties are weakened gradually when the stresses in the elements meet the specific failure criterion. The displacement-controlled loading scheme is used to simulate the complete failure process of reinforced concrete. The analyses focus on the failure mechanisms of the concrete and reinforcement. The complete process of the fracture for the plain concrete prism and the fracture initiation, infilling and saturation of the reinforced concrete prism is reproduced. It agrees well with the theoretical analysis. Through 3D numerical tests for the specimen, it can be investigated the interaction between the reinforcement and concrete mechanical properties in meso-level and the numerical code is proved to be an effective way to help thoroughly understand the rule of the reinforcement and concrete and also help the design of the structural concrete components and systems.