Differing from the standing-wave mode, which is usually observed in a linear cavity configuration, a type of geometric ring mode can self-sustain in a multi-element linear cavity with axial pumping. When the configurations are adjusted in a way that the marginal boundary of the stable region is associated with the self-imaging condition, the off-axis aberration and symmetric breaking with respect to the optical axis results in the existence of a ring trajectory within the cavity. Trigonometrical ray tracing based on numerical simulations showed good agreement with the experimental results.