This chapter explores rock behavior and failure theories in geomechanics, focusing on stress and strain. It distinguishes between brittle fracture and viscous flow in rock failure, crucial for geological stability and engineering. Key theories like Maximum Principal Stress, Maximum Principal Strain, and Maximum Shear Stress are examined for predicting failure across conditions. Practical applications in engineering and geological assessments are highlighted, alongside critiques of theory limitations. The chapter emphasizes refining rock mechanics principles for structural safety and managing geological risks. The Coulomb-Navier Theory explains material failure by comparing shear stress to cohesive strength and frictional resistance, offering insights into failure on specific planes under stress. The Haigh Theory correlates material failure with accumulated strain energy surpassing a critical threshold, crucial for understanding elastic behavior prior to yielding. The Von-Mises Criterion predicts yielding in isotropic and ductile materials by comparing distortional energy to yield strength. Mohr's Theory predicts failure in brittle materials based on principal stresses, distinguishing between tensile and compressive strengths. The Griffith Theory links crack formation in tensioned materials to energy required for surface creation, essential for understanding brittle failure.