Non-axisymmetric RF cavities can produce axially asymmetric acceleration fields. Conventional method using numerical 3-D field tracking to address this feature is time-consuming and thus not appropriate for on-line beam tuning applications. In this paper, we develop analytical treatment of non-axisymmetric RF cavities. Multipole models of cavities are derived using realistic 3-D field in both longitudinal and transverse dimensions. Then, beam dynamics formulism is established. Finally, special case of FRIB quarter-wave resonators are calculated by the model and benchmarked against 3-D field tracking to ensure the efficiency and accuracy of the model.