An apparatus for cladding the interior surfaces of a curved pipe section includes a flexible track that is positioned longitudinally within the curved pipe and supported at opposite ends to corresponding opposite ends of the curved pipe. The flexible track is caused to bend and conform to the radius of curvature of an interior surface of the curved pipe. A robotic crawler is supported on the track section and carries a material applicator head. The robotic crawler is driven back-and-forth across the track section while the material applicator head applies an overlay material to the interior surface of the curved pipe. In a method, the position of the curved pipe in space, the travel direction and speed of the crawler and the position of the application head are all coordinated to maintain the application of the overlay material in the “flat plane” position.