Humberside Police say the burglary the sheep and three, four-week-old lambs were taken from a farm on Holme Lane, Messingham near Scunthorpe.
A barn was broken into between 6pm on Friday, March 1 and 7am on Saturday, March 2.
A sheep and three, four-week-old, lambs were taken and the animals' skins and carcasses were found nearby.
Damage was also caused to the farm and its fencing during the burglary.
A spokesperson for Humberside Police said: "This is clearly a very upsetting incident and the theft of livestock from farms is a serious matter.
"We are investigating this case, looking for forensic evidence and viewing CCTV to try and identify those responsible.
"We have increased patrols in the area and would ask that anyone who sees anything suspicious to call us, we want to catch those responsible and prevent further rural crime."
Anyone with information about this incident should call police on 101 quoting log 203 02/03/19.