In multibody dynamics, the flexibility effects of each body are captured by using a linear combination of elastic mode shapes. If a co-rotational and co-translating frame of reference is used together with eigenvectors of the unconstraint body, which are free-surface modes, some spatial integrals in the floating frame of reference configuration do vanish. The corresponding coordinate system is the so-called Tisserand (or Buckens) reference frame. In the present contribution, a technique is developed for separating an arbitrary elastic mode shape into a pseudo-free-surface mode and rigid body modes. The generated pseudo-free-surface mode has most of the advantageous characteristics of a free-surface mode, and spans together with the rigid body modes the same solution space as it is spanned by the original mode shape. Due to the fact that, in the floating frame of reference configuration, the rigid body motions are already described by special generalized coordinates, only the resulting pseudo-free-surface modes are finally used to capture the flexibility effects of each body. A result of the generated pseudo-free-surface modes is that some of the spatial integrals do vanish and, thus, the equations of motion are significantly simplified. Two examples are presented in order to illustrate and to demonstrate the potential of the proposed method.