Police are appealing for witnesses after the attempted robbery in Bathgate on Saturday at around 5.30pm.
Two men approached the woman, who was walking her dog on the cycle path near Morrison’s supermarket and the railway bridge.
One of them demanded money while he appeared to hold a knife in the air., however both suspects ran away when the woman’s dog came back to her side.
The men are described as being around 5ft 7 tall and in their late teens or early 20’s.
The man who demanded the money was wearing a black hooded top, dark trousers and white training shoes.
Detective Superintendent Pat Campbell said: “No money was handed over and the victim was unhurt but she was understandably upset by her experience.
“We are keen to speak to anyone who was in the area at the time and remembers seeing anything suspicious.
“Similarly we would also urge anyone with information about this incident to contact police immediately.”
Anyone with information regarding this incident should contact Police Scotland immediately on 101 or through the charity Crimestoppers on 0800 555 111.