Abstract: The concrete aggregate model is a type of three-phase composite material consisting of aggregate, mortar matrix and interface layers. Due to the complexity of the aggregate shape and the disparity in material properties of each phase, the adaptive finite element method is needed to improve the efficiency of the corresponding numerical computation and simulation. The p-version finite element method (FEM) can improve the accuracy of numerical solutions by adaptively increasing the order of the basis functions for those elements near each aggregate interface. This method is of such advantages as less limits on the grid quality, less pre-processing work and the hierarchical feature, etc. In this paper, some geometrical models with different aggregate shapes in two dimensions are firstly generated in ANSYS. Moreover, the corresponding aggregate content can reach approximately 60%. A special p-version adaptive FEM method is then designed and analyzed based on the local error control by using subdomains and grading. The resulting method is applied to the linear and nonlinear finite element analyses of several typical aggregate models. The numerical results show that this method is very efficient for the solution of the aggregate models and the computation accuracy of the numerical solutions near the aggregate interfaces can be greatly improved. A highly efficient computational method is provided for further analyzing the relevant mechanical properties of concrete materials.