Katyusha is a nickname first applied to World War II Soviet multiple rocket launchers: BM-13, BM-8 and BM-31. It can also refer to newer MRLs such as the BM-14, BM-21 Grad, BM-24, BM-27 Uragan, or BM-30 Smerch, to the MRLs of other nations, or to Katyusha rocket ammunition fired singly.
BM-13 on ZiS-6 
The ZiS-6 was the first standard chassis.
BM-13 on ZIS-12 
BM-13N on Studebaker US6 
Starting in 1942, the U.S. Studebaker US6 became standardized for the BM-13N (Normalizovanniy)
BM-13 on ZiS/ZiL-151 
The Soviet ZiS-151, later ZiL-157 replaced the Studebaker after the Second World War
BM-31 on ZIS-12 
310mm rockets M-31, manufactured since 1942, were first launched from static ground devices. Since April 1944 launchers for them were mounted on trucks and named BM-31-12.