They were killed with an air weapon.
Police have launched an investigation into the death of the day-old lambs at a farm in Kingsclere Road, Kingsclere, near Basingstoke, on Friday.
Pc Stephen Rogerson, of Hampshire police, said: “It appears the lambs were shot with an air weapon.
“They were only a day old and out in a field. We are keen to identify the person or people responsible for this cruel and heartless offence.
“Local officers are conducting reassurance patrols in the area and asking that any suspicious activity is reported to us.”