The mechanical properties of proteins/peptides play an essential role in their functionalities and implications, as well as their structure and dynamic properties. Understanding mechanical properties is pivotal to our knowledge of protein folding and the molecular basis of diverse cellular processes. Herein, we present a computational approach using ab initio quantum mechanical calculations to determine the mechanical properties—such as bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio—of a solvated Arg-Gly-Asp (RGD) peptide model. Since this peptide serves as the RGD-directed integrin recognition site and may participate in cellular adhesion, it is considered a promising small peptide for medicinal applications. This successful approach paves the way for investigating larger and more complex biomolecules.