This paper proposes an efficient method for computing the scattered electric field of a reconfigurable intelligent surface (RIS) for multiple configurations, taking into account mutual coupling between unit cells. Unlike existing methods that assume unit cells scatter independently, this method accounts for the collective scattering behavior of unit cells, achieving accuracy comparable to full-wave analysis. The method combines ray tracing with the complex radar cross section (CRCS) of an RIS obtained via full-wave analysis to model wave propagation in realistic, multipath environments with RISs. This approach efficiently addresses three critical aspects of RIS-enabled links: mutual coupling between unit cells, multipath effects due to RIS acting as a diffuse scatterer, and the computational challenge of accounting for varying RIS scattering properties across configurations. The method introduces the concept of an effective unit cell CRCS, which incorporates mutual coupling effects and allows for efficient computation of scattered fields for different RIS configurations. This effective CRCS is derived by comparing the scattered field of an RIS with and without mutual coupling, and it is used to compute the scattered electric fields of an RIS. The method is validated against existing models and full-wave analysis, showing accurate results in predicting scattered field levels along the main lobes of the RIS. It is also applied to model a realistic RIS channel, demonstrating its effectiveness in capturing multipath effects and providing accurate field level predictions. The proposed method significantly reduces computational effort compared to full-wave analysis, as it avoids the need for repeated full-wave simulations for each RIS configuration. Instead, it uses the effective CRCS to compute scattered fields efficiently, making it suitable for analyzing RIS-enabled links with multiple configurations. The method is integrated with ray tracing to account for multipath effects in RIS channels, enabling the modeling of realistic communication scenarios. This approach combines the accuracy of full-wave analysis with the efficiency of ray tracing, providing a computationally feasible solution for RIS-enabled communication systems.This paper proposes an efficient method for computing the scattered electric field of a reconfigurable intelligent surface (RIS) for multiple configurations, taking into account mutual coupling between unit cells. Unlike existing methods that assume unit cells scatter independently, this method accounts for the collective scattering behavior of unit cells, achieving accuracy comparable to full-wave analysis. The method combines ray tracing with the complex radar cross section (CRCS) of an RIS obtained via full-wave analysis to model wave propagation in realistic, multipath environments with RISs. This approach efficiently addresses three critical aspects of RIS-enabled links: mutual coupling between unit cells, multipath effects due to RIS acting as a diffuse scatterer, and the computational challenge of accounting for varying RIS scattering properties across configurations. The method introduces the concept of an effective unit cell CRCS, which incorporates mutual coupling effects and allows for efficient computation of scattered fields for different RIS configurations. This effective CRCS is derived by comparing the scattered field of an RIS with and without mutual coupling, and it is used to compute the scattered electric fields of an RIS. The method is validated against existing models and full-wave analysis, showing accurate results in predicting scattered field levels along the main lobes of the RIS. It is also applied to model a realistic RIS channel, demonstrating its effectiveness in capturing multipath effects and providing accurate field level predictions. The proposed method significantly reduces computational effort compared to full-wave analysis, as it avoids the need for repeated full-wave simulations for each RIS configuration. Instead, it uses the effective CRCS to compute scattered fields efficiently, making it suitable for analyzing RIS-enabled links with multiple configurations. The method is integrated with ray tracing to account for multipath effects in RIS channels, enabling the modeling of realistic communication scenarios. This approach combines the accuracy of full-wave analysis with the efficiency of ray tracing, providing a computationally feasible solution for RIS-enabled communication systems.