Solar laser technology typically requires a highly accurate solar tracking system that operates continuously, which increases energy consumption and reduces the system's lifetime. We propose a multi-rod solar laser pumping approach to enhance solar laser stability under non-continuous solar tracking conditions. Using a heliostat, solar radiation is redirected toward a first-stage parabolic concentrator. At its focus, an aspheric lens further concentrates the solar rays onto five Nd:YAG rods positioned within an elliptical-shaped pump cavity. Numerical analysis using Zemax and LASCAD software showed that the tracking error width at 10% laser power loss for the five 6.5 mm diameter and 15 mm length rods was 2.20°, which is 50% higher than that of the solar laser in previous non-continuous solar tracking experiments. 2.0% solar-to-laser conversion efficiency was also attained.