The transverse pumping of solid-state lasers in a cylindrical rod configuration has been explored both analytically and experimentally. The pumping configuration coupled diode laser arrays to the laser rod through slits in a geometrically reflecting chamber using simple lenses. 50 W of diode lasers in the form of ten 5 W, 1 cm bars were used to pump 2 cm of a Nd: YAG rod. Output powers for 3 mm and 4 mm diameter rods were compared with and without the reflecting multi-pass pump cavity. An increase in output power of 35% was achieved by using the multi-pass cavity, approximately in agreement with expectation. Although threshold pump powers agreed with our analysis, slope efficiencies were much lower than expected, and output powers seemed to saturate at 2.5 W with 35 W incident on the rod. Detailed data on the beam profiles and wavelength distributions of the diode laser bars is also presented.