We present the investigation of diode-side-pumping of Alexandrite slab lasers in a range of designs using linear cavity and grazing-incidence bounce cavity configurations. An Alexandrite slab laser cavity with double-pass side pumping produces 23.4 mJ free-running energy at 100 Hz rate with slope efficiency ~40% with respect to absorbed pump energy. In a slab laser with single-bounce geometry output power of 12.2 W is produced, and in a double-bounce configuration 6.5 W multimode and 4.5 W output in TEM00 mode is produced. These first results of slab laser and amplifier designs in this paper highlight some of the potential strategies for power and energy scaling of Alexandrite using diode-side-pumped Alexandrite slab architectures with future availability of higher power red diode pumping.