In this study, the interaction between two non-radially symmetric camphor particles is theoretically investigated and the equation describing the motion is derived as an ordinary differential system for the locations and the rotations. In particular, slightly modified non-radially symmetric cases from radial symmetry are extensively investigated and explicit motions are obtained. For example, it is theoretically shown that elliptically deformed camphor particles interact so as to be parallel with major axes. Such predicted motions are also checked by real experiments and numerical simulations.