Police were called to Cherry Tree Lodge Farm, Crow Tree Bank, Doncaster, after several were shot overnight.
Six lambs were found dead, with a further six having to be put down due to the extent of their injuries.
At Stoupers Gate farm, near Hatfield, six lambs were shot dead overnight between 21 and 22 March, while a further two had to be put down. Police described the attacks as "sickening".
Insp Mark Payling, from South Yorkshire Police, said the "thoughtless act of violence... had caused outrage amongst the farming community across the region and beyond".
He added: "Both incidents have caused distress and outrage not only in our local communities, but across South Yorkshire."
Twenty lambs have been killed in shootings at neighbouring farms.