To explore the internal damage mechanisms of concrete at the meso-scale level, ABAQUS was conducted secondary development using the Python language. A three-dimensional meso-scale model of concrete with concave-convex aggregates, including the interfacial transition zone, was established. Additionally, a method for directly determining spatial interference of concave-convex aggregates was proposed. Subsequently, the model underwent numerical simulations under quasi-static conditions to validate its reliability. Finally, numerical simulations of uniaxial compression were performed for different aggregate shapes. The results indicate that this method can achieve high-density placement with an aggregate volume fraction of over 60%. The influence on concrete compressive strength is minimal for different aggregate shapes. However, significant effects were observed in terms of inducing crack propagation and volumetric failure in concrete. As the surface concavity-convexity and irregularity of aggregates increase, the degree of compressive damage and failure in concrete progressively deepens. These findings contribute to a more profound understanding of internal damage mechanisms in concrete, providing valuable insights for the design of concrete structures.