Chromium, Neodymium doped Yttrium Scandium Gallium Garnet (Cr,Nd:YSGG) single crystals are designed for diode pumped solid-state lasers radiating in the 3 µm range. Er:YSGG crystals show the perspectiveness of their application alongside with the widely used Er:YAG, Er:GGG and Er:YLF crystals. Flash lamp pumped solid-state lasers based on Cr,Nd and Cr,Er doped Yttrium Scandium Gallium Garnet crystals (Cr,Nd:Y3Sc2Ga3012 or Cr,Nd:YSGG and Cr,Er:Y3Sc2Ga3012 or Cr,Er:YSGG) have higher efficiency than those based on Nd:YAG and Er:YAG. Active elements manufactured from YSGG crystals are optimum for medium power pulse lasers with the repetition rates up to several tens of cycles. The advantages of YSGG crystals compared with YAG crystals are lost when large size elements are used because of the worse thermal characteristics of YSGG crystals.