To design high performance terahertz filters, the optical properties of the subwavelength metallic coaxial aperture arrays were investigated. The characteristics of transmission spectra were simulated by the electromagnetic field simulation software. With the change of the geometrical parameters of the structure, two different transmission peaks appeared. One transmission peak redshifts with the increase of the outer radius or the inner radius of the air annulation, and the influence of the thickness on this peak can be neglected. Another transmission peak moves toward long wavelength with the increase of the out radius of the annulation, or the inner radius, or the thickness. This paper also provides an explanation of the phenomena by means of the localized magnetic polaritons and guided mode resonance based on the distribution of the surface current. According to the magnetic plasmon resonance, the equivalent circuit model of the metamaterial for the incidences of the transverse electromagnetic wave were set up, the effects of geometric parameters and lateral displacement on the resonance conditions were studied by this model. The variation of the array geometry parameters changes the capacitance and inductance of the equivalent circuit, which leads to the shift of the magnetic resonance peak. Comparison of the result of simulation with that of the equivalent circuit model shows that the equivalent circuit models could be useful for structure design and performance analysis of the metamaterial terahertz filters.