The stress tensor, introduced by Cauchy in 1822, is a fundamental concept in continuum mechanics, connecting internal forces to deformation in materials. It plays a central role across physics and engineering, governing elasticity, fluid dynamics (via the Navier-Stokes equations), and field theories, while also linking microscopic particle behavior to macroscopic properties in statistical and condensed matter physics. Theoretical descriptions of stress exist at multiple scales: macroscopic models use empirical constitutive equations; mesoscopic models capture local plastic rearrangements using stochastic rules; and microscopic approaches aim for first-principles expressions based on interparticle forces, though they face challenges due to complex many-body interactions. This internship project aims to develop a microscopic, first-principles theory of the stress tensor in dense materials. It will start from the Irving-Kirkwood formalism and seek a closed-form solution using advanced theoretical methods (mean field theory, stochastic models, projection techniques), supported by numerical simulations (e.g., hard-sphere models) to explore stress fluctuations and redistribution in disordered and nonequilibrium systems.