This paper describes the design of an umbilical-free mobile non-destructive testing (NDT) climbing robot for industrial applications that is capable of inspecting oil tanks, pipelines, petro-chemical tanks, bridges, railways, etc. The mechanical design is based on a wheeled mobile robot with magnetic adhesion forces optimised with flux concentrators. The robot carries a NDT wheel probe in order to detect weld defects, wall thickness and corrosion. The robot adapts to surface curvatures (both convex and concave and both along its length and width) and can make transitions between surfaces that have an angle of up to ninety degrees between them. The robot and an on-board NDT Flaw Detector are controlled remotely via wireless communication. Higher level commands remotely adjust NDT parameters, robot speeds, and control inspection tasks from the ground.