Stochastic mechanics covers the topics of the stochastic structural analysis, random vibration, reliability assessment, reliability-based design optimization, and stochastic optimal control. Traditionally, stochastic response analysis of structures, reliability assessment, and reliability-based design optimization were solved using distinct approaches. Furthermore, there was a lack of unified theory, and efficient and straightforward method for addressing stochastic linear and nonlinear stochastic response analysis, reliability estimation and optimum design problems in static and dynamic structures. Based on the fundamental principle of probability conservation, this study derives and established a unified fundamental equation, namely the probability density integral equation, to characterize the propagation and evolution of randomness in space and time domains for generic stochastic systems. Building upon this equation, statistical moment formulas for stochastic responses, as well as formulas for reliability and its sensitivity are deduced. The unified probability density integral theory is proposed, and direct probability integral method is developed to address stochastic response analysis, reliability assessment, reliability-based design optimization, and optimal control for static/dynamic systems [1–3]. As a versatile and efficient method for stochastic mechanics and structural reliability, the direct probability integral method attacks the challenges in the stochastic static and dynamic analysis of large-scale linear and nonlinear structures with up to 1000 random variables, as well as system reliability and dynamic reliability-based design optimization. Additionally, it is applicable to Gaussian/non-Gaussian, stationary/non-stationary stochastic excitations, and Markov/non-Markov systems, providing powerful computational tools for the reliability and safety assessment, risk management, and digital and intelligent optimal design of large-scale structures.