The present invention relates to a guide rail assembly for securement of a tube cutting apparatus for cutting of boiler tube walls to a fixed point on a tube wall, while allowing lateral repositioning of a cutting tool relative to the tube wall. The assembly includes a guide rail having a convex surface along which a carriage having a cutting device may be fixedly positioned by mating friction engagement of a concave surface of pairs of linear guide blocks secured to the carriage with the convex surface of the guide rail.