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A stochastic response analysis and reliability assessment of subsea free spanning pipeline systems subjected to seismic motion are conducted based on the Monte Carlo simulation method. The ground motion is modeled as a non-stationary random process possessing a time-modulated Kanai-Tajimi seismic power spectrum. Further, the spanning pipeline system is modeled as a multi-degree-of-freedom (MDOF) system. Nonlinear hydrodynamic effects are modeled based on Morison's theory. Furthermore, employing the concept of spectral representation of random processes, realizations compatible with the prescribed excitation evolutionary power spectrum are generated. Then, response statistics are derived by considering the ensemble of the response realizations obtained via a standard fourth order Runge-Kutta numerical scheme for solving (nonlinear) ordinary differential equations. Advantages of the presented method over alternative ones are highlighted. Also, differences between the method presented and contemporary code provisions/industry standards are thoroughly investigated and discussed. The potential benefits from incorporating a stochastic framework for risk assessment and reliability-based design vis-à-vis traditional/conventional treatments are illustrated. Realistic examples are considered to demonstrate the applicability of the methodology.