She was last seen at her home on May 19 and was reported missing on May 24. Officers' attempts to locate her have raised fears for her welfare, police said.
They believe she left home without her medication, mobile phone or bank card.
A statement from North Yorkshire Police said: "As part of our ongoing enquiries to locate her, we are carrying out house and neighbourhood searches, trawling CCTV, checking with hospitals and with trains, buses and taxi companies for any signs of Rachel.
"It is understood that she usually travels by train. British Transport Police is providing support.
"To assist the missing person investigation, we are also appealing to the public for any possible sightings during the past seven days or any information that could help us to find Rachel."
Anyone with information is asked to call 101 and quote reference number 12220089091. Anyone who sees Rachel is asked to calll 999 immediately.