Analytical expressions for the spot size and the Kerr-lens mode-locking (KLM) strength can be represented as explicit functions of the position in the cavity, the laser power, and the stability parameter for a four-mirror figure-Z laser resonator. The results indicate that the KLM strength achieves its maximum value at the edge of the stability range. Self-amplitude modulation and group-velocity dispersion compensation can be established by a prism pair. Simultaneously obtaining a large pumping efficiency and KLM is possible for this cavity.