Recycled rubber concrete (RRC), a sustainable building material, provides a solution to the environmental issues posed by rubber waste. This research introduces a sophisticated hybrid random aggregate model for RRC. The model is established by combining convex polygon aggregates and rounded rubber co-casting schemes with supplemental tools developed in MATLAB and Fortran for processing. Numerical analyses, based on the base force element method (BFEM) of the complementary energy principle, are performed on RRC’s uniaxial tensile and compressive behaviors using the proposed aggregate models. This study identified the interfacial transition zone (ITZ) around the rubber as RRC’s weakest area. Here, cracks originate and progress to the aggregate, leading to widespread cracking. Primary cracks form perpendicular to the load under tension, whereas bifurcated cracks result from compression, echoing conventional concrete’s failure mechanisms. Additionally, the hybrid aggregate model outperformed the rounded aggregate model, exhibiting closer peak strengths and more accurate aggregate shapes. The method’s validity is supported by experimental findings, resulting In detailed stress–strain curves and damage contour diagrams.