A member for a high pressure fluid or a member for a high pressure fluid with a built-in slider having higher quality which can be provided at a low price, and by which the generation of tensile stress in the lower end inner peripheral edge part of a branch hole can be canceled by compressive residual stress to be effectively restrained, the internal pressure fatigue strength in the branch hole part can be improved to be excellent in durability, prevent a fluid leakage due to the occurrence of cracks and then exhibit a sure and stable function, further only the addition of the pressing force applying process to the ordinary manufacturing process will be sufficient, and complicated equipment is not required to hardly cause the problems of an increase in the equipment cost due to an increase in the number of processes and lowering of productivity. The method of forming a branch hole communicating with a hollow part in a member for a high pressure fluid having the hollow part, which is characterized in that before or after, or simultaneously with a process of pressing inward the member for a high pressure fluid from the outside to form a part where compressive stress remains on the hollow part side inner peripheral surface, a process of boring a branch hole opened to the hollow part is executed to make the compressive residual stress exist in the peripheral edge of the branch hole, and a branch hole part of a member for a high pressure fluid formed by the described method.