Low lamp input-to-TEM₀₀ mode laser output conversion efficiency and strong thermal lensing effects are bottleneck issues in commercially available single-rod/single-beam lamp-pumped lasers. A six-rod/six-beam concept is proposed to substantially enhance lamp input-to-TEM₀₀ mode laser output conversion efficiency. A 4-kW-single-thick arc lamp was used to efficiently pump six thin Nd:YAG rods simultaneously within a modified two-ellipse pump cavity. All of the design parameters were numerically optimized by Zemax^® and LASCAD^® software. Since each rod absorbed only a small part of the lamp power, significantly reduced thermal lensing and thermal stress problems were predicted. Asymmetrical laser resonators were adopted to enable a large mode-matching between the lamp pump mode and the fundamental laser mode within each rod. 34.82-W total TEM₀₀ mode laser power was numerically calculated, corresponding to 0.87% lamp input power-to-TEM₀₀ mode laser power conversion efficiency and a 2.18 times improvement over that of the state-of-the-art lamp-pumped laser. A TEM₀₀ mode power-to-multimode power ratio of 59.0% was also obtained, being 2.40 times more than that of the most efficient single-rod TEM₀₀ mode lamp-pumped laser. Six TEM₀₀ mode laser beams emitting from the single laser head may provide a cost-effective laser solution to several processes in industry and scientific research. For the extraction of a single TEM₀₀ mode laser beam, a laser resonant cavity with folding mirrors was also presented. A 15.34-W laser beam brightness figure of merit was numerically calculated, corresponding to a 13-fold increase over that from each of the six TEM₀₀ mode laser beams.