Abstract: Flexible composite structures are widely used in large-scale structures, such as those in aeronautics and astronautics. These structures can be regarded as combinations of beam, plate, and solid components. The geometric nonlinearities of slender flexible components can induce complex nonlinear dynamic behaviors, including the softening and hardening characteristics of backbone curves and the coexistence of multiple periodic solutions in forced responses at a given excitation frequency. Although finite element modeling provides a powerful tool for analyzing such structures, it often relies on a single solid element type due to the difficulty in handling constraints between different element types (e.g., beam, plate, and solid elements). As a result, the resulting finite element models may contain many redundant degrees of freedom, which significantly increase the computational cost. To account for the geometric characteristics of substructures, different types of elements are employed to model substructures in a composite structure, and proper constraints are imposed on the coupled interfaces between different substructures via the multi-point constraint formulation and the Lagrange multiplier method. Consequently, the governing equations of the integrated structure can be expressed in the form of differential-algebraic equations (DAEs). This enables the computation of the associated spectral submanifolds (SSMs), which are utilized to construct reduced-order models for efficiently analyzing the nonlinear dynamic responses of the structures, including backbone curves and forced response curves under harmonic excitations. To demonstrate the proposed strategy, three typical composite structures, namely solid–beam, solid–plate, and beam–plate structures, are presented as numerical examples. Compared with single-solid-element modeling, the results show that the proposed hybrid-element DAE formulation significantly improves the computational efficiency of the SSM-based model reduction while maintaining high accuracy in the computation of dynamic responses including backbone and foreced response cruves. Thus, this work provides a foundation for the efficient application of SSM-based model reduction to complex large-scale flexible composite structures.