Polycrystalline aggregates are made in a wide array of geometric configurations (thin wire, thin film, and bulk configurations, to name a few) for engineering applications. Various elastic moduli have been reported for these configurations. The inconsistence of Young’s modulus has been attributed to micro-defects and microscopic texture in the existing open literature. In the present study, the modulus variation of the polycrystalline aggregates in various geometric configurations is explained from a new perspective, i.e., the constraint and interaction among the grains. A finite element scheme with statistic consideration based on the Central Limit Theory is employed to systematically investigate the effective Young’s modulus of the polycrystalline copper aggregates in various geometric configurations. The correlation between the effective modulus of the polycrystalline copper and the geometric configuration is fully pictured. For the polycrystalline copper, the spread of the effective modulus due to the geometric configuration could be as large as 20%.