The numerical simulation of the optical resonator for a coaxial slab CO₂ laser is conducted. The resonator consists of a toric mirror, a w-axicon, and a plane output coupler. To hold the two slabs coaxially, struts exist in the annular gap region. The effects of the struts on the output power and beam quality for the given resonator are discussed. It is found that varying the vertex of the toric mirror can control the oscillation mode between the E₀₀ fundamental mode and the E₀₁ first azimuthal mode. It is revealed that the resonator loss of the fundamental mode can be smaller than the first azimuthal mode by shifting the vertex inward, and this results in single-mode oscillation at the E₀₀ fundamental mode. On the other hand, the maximum output is obtained under conditions where the resonator oscillates at the E₀₁ mode, because the nodes of the mode coincide with the position of the struts. Loss measurement of each eigenmode well describes the aforementioned phenomena.