Abstract: A tubular longitudinal clamp is used to fix thermal insulation along piping within the clamp. The clamp comprises an open tubular body having one end with a larger diameter than the other end so that the tubular clamps can be fitted together by insertion of the smaller diameter end of one clamp into the larger diameter end of a second clamp. An embodiment of the invention includes a thermal insulation system for high or low temperature piping. Insulating material in parts of several lengths or helicoidal application with a width identical to the perimeter of an industrial pipe is installed on the pipe and is clamped thereto with a series of open tubular clamps mated one to the other.