The stochastic finite element method (SFEM) is a powerful computational tool in stochastic mechanics for analyzing systems with uncertain properties. It extends the classical deterministic finite element method to handle stochastic (static and dynamic) problems involving random material, geometric, and loading properties. SFEM is used to solve stochastic partial differential equations (PDEs) and has gained significant attention due to advances in computational power, enabling efficient treatment of large-scale problems. This review summarizes past and recent developments in SFEM, discusses its applications, and identifies future research directions. SFEM involves modeling uncertainties in system parameters using stochastic processes and fields. Two main methods for simulating these processes are the spectral representation method and the Karhunen–Loève (K–L) expansion. The spectral representation method expands stochastic fields using trigonometric functions with random phase angles and deterministic amplitudes, while the K–L expansion represents fields as a series of eigenfunctions derived from the autocovariance function. Both methods are used to generate sample functions that approximate the target stochastic fields. For non-Gaussian processes, methods such as correlation distortion and polynomial chaos (PC) expansions are employed. Correlation distortion methods involve transforming Gaussian fields to non-Gaussian ones, while PC expansions use orthogonal polynomials to represent the stochastic response. These methods are used to simulate non-Gaussian fields with prescribed statistical properties. SFEM is applied to various engineering problems, including structural, fluid, and acoustic systems. It involves discretizing stochastic fields, formulating the stochastic finite element matrix, and calculating response statistics. Monte Carlo simulation (MCS) and the perturbation method are two common approaches for calculating response variability. MCS is a robust method for verifying the accuracy of other approaches, while the perturbation method uses Taylor series expansions to approximate the response. The spectral stochastic finite element method (SSFEM) is a variant of SFEM that uses polynomial chaos expansions to represent the response. SSFEM is particularly effective for problems with smooth autocovariance functions and has been shown to provide accurate results with a small number of terms. The review also discusses challenges in simulating non-Gaussian fields, including the need for accurate marginal probability distributions and the computational cost of high-dimensional problems. Future research directions include improving the efficiency and accuracy of simulation methods, developing specialized software for SFEM, and applying SFEM to complex engineering systems with uncertain parameters.The stochastic finite element method (SFEM) is a powerful computational tool in stochastic mechanics for analyzing systems with uncertain properties. It extends the classical deterministic finite element method to handle stochastic (static and dynamic) problems involving random material, geometric, and loading properties. SFEM is used to solve stochastic partial differential equations (PDEs) and has gained significant attention due to advances in computational power, enabling efficient treatment of large-scale problems. This review summarizes past and recent developments in SFEM, discusses its applications, and identifies future research directions. SFEM involves modeling uncertainties in system parameters using stochastic processes and fields. Two main methods for simulating these processes are the spectral representation method and the Karhunen–Loève (K–L) expansion. The spectral representation method expands stochastic fields using trigonometric functions with random phase angles and deterministic amplitudes, while the K–L expansion represents fields as a series of eigenfunctions derived from the autocovariance function. Both methods are used to generate sample functions that approximate the target stochastic fields. For non-Gaussian processes, methods such as correlation distortion and polynomial chaos (PC) expansions are employed. Correlation distortion methods involve transforming Gaussian fields to non-Gaussian ones, while PC expansions use orthogonal polynomials to represent the stochastic response. These methods are used to simulate non-Gaussian fields with prescribed statistical properties. SFEM is applied to various engineering problems, including structural, fluid, and acoustic systems. It involves discretizing stochastic fields, formulating the stochastic finite element matrix, and calculating response statistics. Monte Carlo simulation (MCS) and the perturbation method are two common approaches for calculating response variability. MCS is a robust method for verifying the accuracy of other approaches, while the perturbation method uses Taylor series expansions to approximate the response. The spectral stochastic finite element method (SSFEM) is a variant of SFEM that uses polynomial chaos expansions to represent the response. SSFEM is particularly effective for problems with smooth autocovariance functions and has been shown to provide accurate results with a small number of terms. The review also discusses challenges in simulating non-Gaussian fields, including the need for accurate marginal probability distributions and the computational cost of high-dimensional problems. Future research directions include improving the efficiency and accuracy of simulation methods, developing specialized software for SFEM, and applying SFEM to complex engineering systems with uncertain parameters.