To provide a fitting structure for a bracket which has sufficient assured strength even in the event of using overhang caulking.

A diameter-reduced portion 15 is formed beforehand on the outer circumferential face of the tube 3 of the cylinder equipment for a suspension. The diameter-reduced portion 15 and a knuckle bracket 10 for coupling with a car body are joined with the overhang caulking in a state that the knuckle bracket 10 fits into the diameter-reduced portion 15. Most of the caulked portions 20 enhance peel strength by forming first joining portions 21 where overhang portions on the tube side and overhang portions on the bracket side bite into each other. Shear force is resisted by steps 16 placed on both sides of the diameter-reduced portion 15 and a second joining portion 22 with a counterface for fitting.