This study aims to investigate the inherent anisotropy of concrete during compressive tests by examining different material orientations (MOs) and mechanical parameters. Specifically, the study focuses on the compressive strength, compressive fracture energy, and failure angles of concrete samples with varying maximum coarse aggregate sizes (MCASs) across different MOs. To achieve consistent compressive strength, three normal concrete mixtures were prepared using rounded MCASs of 4.75 mm, 9.5 mm, and 19 mm. The study involved casting unreinforced concrete cubes and lintels, as well as three standard cylinders for each MCAS (100 mm diameter and 200 mm height). After 28 days of water curing, 75 samples (54 mm diameter and 97 mm height) were drilled from the concrete cubes and lintels at orientations of 0°, 22.5°, 45°, 67.5°, and 90°. The results showed that the compressive strength of the concrete samples significantly decreased due to the drilling process, with core samples oriented at 0° experiencing a reduction in compressive strength ranging between 10.8–13.9% compared to the standard samples for all sizes. Additionally, the study revealed that compressive strength and compressive fracture energy are greatly influenced by MCAS and MO. As the MCAS increases, compressive strength increases while compressive fracture energy decreases. Compressive strength varies based on MO, with the lowest strength occurring at a 45° angle with a 4.75 mm aggregate, and the highest strength at a 0° angle with a 19 mm aggregate. The compressive strength for 19 mm samples decreased by 8.8% with changes in drilling angles, while for 9.5 mm and 4.75 mm samples, the strength decreased by 14.6% and 15.2%, respectively. The highest compressive strengths were recorded for 19, 9.5, and 4.75 mm aggregate sizes, respectively.