The main goal of this paper is to present an automatic approach for the dynamic modeling of the oblique impact of a multi-flexible-link robotic manipulator. The behavior of a multi-flexible-link system confined inside a closed environment with curved walls can be completely expressed by two distinct mathematical models. A set of differential equations is employed to model the system when it has no contact with the curved walls (Flight phase); and a set of algebraic equations is used whenever it collides with the confining surfaces (Impact phase). In this article, in addition to the Assumed Mode Method (AMM), the Euler-Bernoulli Beam Theory (EBBT), and the Newton’s kinematic impact law, the Gibbs-Appell (G-A) formulation has been employed to derive the governing equations in both phases. Also, instead of using 3 x 3 rotational matrices, which involves lengthy kinematic and dynamic formulations for deriving the governing equations, 4 x 4 transformation matrices have been used. Moreover, for the systematic modeling of flexible multiple links through the space, two virtual links have been added to the n real links of a manipulator. Finally, two case studies have been simulated to demonstrate the validity of the proposed approach.