A caliper for disc brakes, comprising: an inner caliper section and an outer caliper section which are disposed by opposing to each other by sandwiching a disc rotor therebetween and both ends thereof in length directions are linked integrally via a bridge section; and pressurizing piston hydraulic cylinders which are provided to respective opposing surface regions of the inner caliper section and the outer caliper section and simultaneously pressurize the disc rotor from both surfaces thereof via brake pads when in an action, wherein: the hydraulic cylinder on the inner caliper section side and the hydraulic cylinder on the outer caliper side are linked by cylinder-side hydraulic channels (16, 17) provided on respective back face sides and a hydraulic linking channel provided inside the bridge section; and each of the cylinder-side hydraulic channels (16, 17) and the hydraulic linking channel are formed by setting to be in a state embedded simultaneously in each of the caliper sections (12, 13) and the bridge section when integrally casting-molding each of the caliper sections (12, 13) and the bridge section through providing a connecting channel forming section for each of the cylinder-side hydraulic channels (16, 17) and a connecting channel forming section for the hydraulic linking channel in advance in a core used when casting-molding the inner caliper section, the outer caliper section, and the bridge section, the both end sections of the connecting channel forming section for the hydraulic linking channel being linked, respectively, to the end sections of the connecting channel forming sections for the cylinder-side hydraulic channels (16, 17), wherein at a connection point between one end section of the connecting channel forming section for the hydraulic linking channel on the inner caliper unit side and one end section of the connecting channel forming sections for the cylinder side hydraulic channels (16, 17), an inside space is formed, characterized in that a bleeder hole for releasing air is opened to be linked to the hydraulic linking channel in the inner caliper unit from the outer surface thereof towards the hydraulic linking channel, wherein the bleeder hole and the hydraulic linking channel are formed in such a manner that the positions of the center lines thereof are shifted from each other and wherein the bleeder hole and the hydraulic linking channel are linked to each other in a sufficiently overlapping manner via the inside space. the hydraulic cylinder on the inner caliper section side and the hydraulic cylinder on the outer caliper side are linked by cylinder-side hydraulic channels (16, 17) provided on respective back face sides and a hydraulic linking channel provided inside the bridge section; and each of the cylinder-side hydraulic channels (16, 17) and the hydraulic linking channel are formed by setting to be in a state embedded simultaneously in each of the caliper sections (12, 13) and the bridge section when integrally casting-molding each of the caliper sections (12, 13) and the bridge section through providing a connecting channel forming section for each of the cylinder-side hydraulic channels (16, 17) and a connecting channel forming section for the hydraulic linking channel in advance in a core used when casting-molding the inner caliper section, the outer caliper section, and the bridge section, the both end sections of the connecting channel forming section for the hydraulic linking channel being linked, respectively, to the end sections of the connecting channel forming sections for the cylinder-side hydraulic channels (16, 17), wherein at a connection point between one end section of the connecting channel forming section for the hydraulic linking channel on the inner caliper unit side and one end section of the connecting channel forming sections for the cylinder side hydraulic channels (16, 17), an inside space is formed, characterized in that a bleeder hole for releasing air is opened to be linked to the hydraulic linking channel in the inner caliper unit from the outer surface thereof towards the hydraulic linking channel, wherein the bleeder hole and the hydraulic linking channel are formed in such a manner that the positions of the center lines thereof are shifted from each other and wherein the bleeder hole and the hydraulic linking channel are linked to each other in a sufficiently overlapping manner via the inside space.