Dielectric resonator is a kind of important building block for metamaterials. Here, we numerically investigated the resonance modes excited in the dielectric resonator whose cross section has different ratios of the length to width. It is found that the cross-sectional aspect ratio has great influence on the excitation sequence of the resonance modes. The magnetic resonance mode is firstly excited for the aspect ratio smaller than 2.2, whereas it is excited at the second resonance for the ratio lager than 2.2. As the turning point, i. e. with the aspect ratio of 2.2, the magnetic mode cannot be achieved. The calculations also show that the magnetic resonance can be tuned by adjusting the direction of the incident electromagnetic wave, thus achieving the polarization control of electromagnetic response. This study provides valuable information for the design and research of novel dielectric-based metamaterials.