Creep deformation, a time-dependent material response under sustained stress, plays a critical role in the long-term performance and reliability of structural components, particularly at elevated temperatures. This article presents a mathematically rigorous analysis of creep deformation mechanisms and a phenomenological framework to describe its stages and evolution. By coupling microstructural insights with continuum mechanics, we derive and validate constitutive models capturing the interplay of stress, temperature, and material properties. The analysis integrates diffusion kinetics, dislocation dynamics, and grain boundary phenomena into a unified formalism, ensuring precision in predicting creep behavior across a wide spectrum of materials.