In order to study the mesomechanical properties of recycled aggregate concrete (RAC) under uniaxial tension, a numerical model of RAC with two different aggregate shapes (circular and convex) and five different replacement ratios of recycled aggregate (0, 30, 50, 70, and 100%) was established. A new finite element method-base force element method (BFEM) was used to derive the element strain and the element stiffness matrix with an explicit expression without Gauss integral. The two-dimensional numerical model of the RAC was simulated to study the effect of aggregate shape, replacement ratio of recycled aggregate, aggregate distribution and interfacial transition zone (ITZ) properties on mesomechanical properties of RAC. Simulation results demonstrated that once the first crack appeared, the peak stress and peak strain were reached. The first crack appeared in old ITZ, which was located in whether the upper part or the lower part of the large-size recycled aggregate. The continuous cracks were mainly around the recycled aggregate and the aggregate concentrated area. Comparing with natural concrete, when the replacement ratio of recycled aggregate was 100%, the elastic modulus decreased by 16~25%, the peak stress decreased by 12~15%, and the peak strain changed slightly. The ITZ had a significant influence on the mechanical properties of RAC and must be considered in the analysis.