During one incident Lyndsey Dimmock, from the New Hall Lane area of Preston, is alleged to have produced a weapon and threatened a member of staff who challenged her with it.
The shoplifting offences under investigation all took place at retail parks around Preston within the last month.
Sgt. Hesketh of Lancashire Constabulary said: "I ask that anyone connected to retail staff and security in Preston ensure store managers and other staff members are made aware of this woman, and keep her picture in a staff area in case she is seen so that we can be contacted.
"Lyndsey, I appeal to you directly - these matters won't go away until we have spoken to you and officers will continue to look for you until we find you.
"Hand yourself in to Preston Police Station."
Call on 01772 209643 with information or email Sgt. Hesketh on [email protected]
Alternatively, call Crimestoppers anonymously on 0800 555 111.