York Magistrates’ Court issued arrest warrants after both men failed to attend court to face separate theft charges in November.
Nicholson was due to face Magistrates on 18 November charged with stealing a bike form Parliament Street and resisting arrest.
Rawcliffe was due in court on 9 November to answer a charge of stealing food and drink from the Coop on Moorcroft Road.
Police have made enquiries in and around York but are now appealing to the public to help locate the two men.
Sergeant Fiona Willey, of York Safer Neighbourhood Team, said:
Both Richard Nicholson and Matthew Rawcliffe have shown a blatant disregard for the criminal justice system and I am appealing to the public to help us find them so they can attend court and face up to the charges against them.
We believe that both men are still in the York area and I urge the public to keep their eyes peeled and let the police or Crimestoppers know if they see them around.
Anyone who has any information that can help the police with their enquiries is urged to contact York Police on 101.
Alternatively, Crimestoppers can be contacted anonymously on 0800 555 111.