CLASSI and SASSI are two sub-structuring approaches to analyze the phenomena of soil-structure interaction (SSI) with extensive applications in the nuclear power industry. Many similarities exist in the two methods; both approaches treat the SSI problem as a linear problem (soil and structure are modeled as behaving linearly), solve the problem in the frequency domain, and treat complex free-field wave propagation mechanisms, including incoherence of ground motion. SASSI has distinct advantages in modeling embedded foundations of irregular shapes, including foundation flexibility. Standard versions of CLASSI treat the foundation of the structures as behaving rigidly with respect to earthquake motions and the calculation of overall response. Structures are modeled in CLASSI using their fixed-base eigen-system. This permits very detailed structure models of 100,000s degrees of freedom represented by 1000s of fixed-base modes to be incorporated directly into the SSI analysis. Other advantages of CLASSI are the ability to interrogate sub-structure elements of the problem efficiently, and the ability to cost-effectively perform probabilistic response analyses of soil-structure systems. The limitation of CLASSI is its inability to treat embedded foundations of complex geometry and the assumption of rigid foundation behavior. This paper summarizes the general CLASSI approach to the SSI problem. Next, a Hybrid approach to developing SSI parameters is presented, whereby the advantages of SASSI for foundation modeling are used in the development of foundation impedances and scattering functions for embedded foundations and analysis in CLASSI. The computer program RIGID is validated and verified against published results. An application to the modeling of the SSI parameters for the Mühleberg Nuclear Power Plant Reactor and SUSAN Buildings is presented.