Denise Birdsall, aged 52, left her homein Garforth at about 9.30am today, and officers are concerned for her welfare.
She was last seen wearing pink tracksuit bottoms, a baggy lilac jumper and black trainers.
An investigation has found that at 10:31am she boarded a Scarborough-bound train from Leeds railway station and arrived in the seaside town at 11.42am.
Detective Inspector James Entwistle, of Leeds District CID, said: “We are very concerned for Denise’s welfare and urgently need to trace her and check that she is okay.
“We would like to hear from anyone who has seen her in the Scarborough area or anywhere else that she may have gone since arriving there by train this morning.”
Anyone with information is asked to contact Leeds District CID via 101, quoting log number 585 of July 16.