Voids in materials, whether introduced unintentionally during manufacturing or intentionally for specific applications, can significantly alter mechanical behavior. This study presents a method for modeling the elastic response of multibody systems containing voids by combining the finite element method with an alternative analytical mechanics approach based on Maggi’s equations. Compared to classical Lagrange’s equations, Maggi’s formalism simplifies the derivation of motion equations for elastic multibody systems, particularly under nonholonomic constraints, reducing computational effort without compromising accuracy. The approach is demonstrated on a rectangular bar with void fractions from 1 to 4%, showing that even the small void content can markedly affect displacements and mechanical properties. The proposed methodology provides an efficient framework for predicting the behavior of complex materials with microstructural irregularities, offering practical insights for engineering applications where voids influence performance and durability.