The dynamic behavior of a rotating machine consists not only of the response of the shaft, but it also contains information of all supporting structures and equipment interacting with the rotor. These support structures, also named foundations, can add substantial influence on the machine operational behavior, hence it becomes necessary to dynamically characterize its components. This study presents the application of substructuring techniques in assembling a supporting structure model for a rotating machine and presents a novel formulation of the mixed coordinates method, which is used to connect rotor and foundation. This foundation model is validated against the actual physical foundation and provides an efficient way to analyze and optimize the behavior of such systems. The robustness of the substructuring technique is demonstrated by comparing the responses of the global system solved with both the dynamically assembled and experimentally measured supporting structures in free-free and clamped conditions. The simulations reveal important phenomena of the complete system, including the presence of structural modes in the Campbell diagrams and in displacement responses. The technique allows flexibility in the design of numerical foundations without requiring physical mounting and measurements.