Linzi Davis, 36, and son River Bain, from the village of Auldearn, were last seen close to Nairn railway station in the Scottish Highlands on Friday.
Officers said they had made no contact with family or friends and are anxious to find them.
It is thought the pair have links with Nairn, Inverness and Forres, and it is also possible they have travelled to Edinburgh on public transport, Police Scotland said.
Ms Davis is 5ft 2ins with a medium build and dark brown hair worn in a side parting.
She has tattoos on the top of her right arm and on her collar bone.
River is described as slim with short dark hair.
It is not known what they were wearing when last seen.
A force spokesman said: “Police are anxious to trace Linzi and River to ensure they are safe and well and urge anyone who may have information on their whereabouts to make contact with police on 101.”
Officers also appealed directly to Ms Davis to make contact by phoning 101 or via any police officer or police station.