<p>Flexible multibody systems pertain to the analysis of the dynamic behaviour of a system comprising numerous bodies, whereby at least one body exhibits the ability to undergo deformation. In spatial engineering applications, 3D beams are commonly used to model deformable bodies. There are different methods to model structural flexibility; the most applicable approaches within the multibody system framework are the Floating Frame of Reference formulation (FFR) and the Absolute Nodal Coordinates formulation (ANCF). One notable advantage of the ANCF, in contrast to the FFR, is its ability to represent the slope discontinuities that may exist in flexible structures. Nevertheless, the ANCF is suited for continuum behaviour with large deformation problems. The paper presents a systematic procedure for modelling slope discontinuities and proposes a semi-continuum formulation that is suitable for applications involving discontinuous structures and are subjected to restricted deformations. This formulation still captures the essential dynamics introduced by the elasticity of multibody system components. A simplified form of strain tensor has been utilized, by which, the resulting stiffness matrix is linear in the local frame of the beam element. Static, dynamic and modal analysis of the spatial double pendulum structure of 3D-Beam with circular cross-section is carried out to demonstrate the effectiveness of the proposed formulation. Operational Modal Analysis (OMA) is employed for modal analysis, and the experimental study shows that all of the extracted frequencies agree successfully with the semi-continuum formulation. In addition, the paper clarifies the limitations of using the tangent stiffness matrix to depict a linearized form of an ANCF, explains the challenge of extracting close frequencies using the OMA, and proposes strategies to overcome this obstacle.</p>