Masham is a market town and civil parish in the former Harrogate district of North Yorkshire, England. It had a population of 1,205 at the 2011 …Masham is a market town and civil parish in the former Harrogate district of North Yorkshire, England. It had a population of 1,205 at the 2011 census. In Wensleydale, on the western bank of the River Ure, the name derives from the Anglo-Saxon "Mæssa's Ham", the homestead belonging to Mæssa.