A caliper for a disc brake comprising a piston accommodated within a cylinder of a caliper body of the disc brake such as to be capable of pressing on a braking pad, wherein: - said piston having a piston outer surface suitable to co-operate with a cylinder inner surface of the caliper body which accommodate the piston, said outer surface having a predefined piston diameter (Dp) and said cylinder inner surface having a predefined cylinder diameter (Dc), wherein said piston comprises a piston body and a head thereof suitable to press against the pad, the piston comprising: - a sheathing housing being arranged on the head of the piston having housing walls and a first opening suitable to directly face the cylinder and a second opening suitable to directly face the braking pad; and wherein the caliper further comprising a flexible sheathing for the protection of a piston-cylinder unit for a disc brake capable of being arranged in a retracted condition and in an extended condition, said flexible sheathing being associated with said piston; said flexible sheathing comprising: - a sheathing body developing from an inner diameter (Di) to an outer diameter (De) and defining an axial direction (I-I), a radial direction orthogonal to the axial direction and a circumferential direction; said sheathing body comprising: - a first hooking ring being arranged along the outer diameter (De) of the sheathing which projects in the axial direction and is suitable to be fixed to a caliper body; - a second hooking ring being arranged along the inner diameter (Di) of the sheathing; - a sheathing portion (Pg) which extends from said inner diameter (Di); - said body comprises a joining band, said joining band extending substantially in a planar manner in the radial direction in the shape of a disc; wherein: - the joining band extends in the radial direction by a predefined second extension or radial extension of joining band; - said second hooking ring projects in the axial direction and is suitable to be fixed to the piston; - the sheathing comprises a plurality of folds separated from said second hooking ring and made up by folds being defined by portions of said sheathing body that are folded such as to have the surfaces thereof directly facing each other and such as to allow the extension of the sheathing during the outward movement of the piston from the cylinder of the caliper body; said plurality of folds being totally arranged on said sheathing portion (Pg) extending from the inner diameter (Di); - said joining band connects the first hooking ring to the plurality of folds; - the plurality of folds extends in the radial direction by a predetermined first extension or radial extension of folds; - said sheathing housing of the piston entirely accommodates said plurality of folds of the sheathing, thereby avoiding that a housing for the plurality of folds should be provided within the caliper body characterised in that said predetermined second extension results to be equal to or greater than said predetermined first extension. - said piston having a piston outer surface suitable to co-operate with a cylinder inner surface of the caliper body which accommodate the piston, said outer surface having a predefined piston diameter (Dp) and said cylinder inner surface having a predefined cylinder diameter (Dc), wherein said piston comprises a piston body and a head thereof suitable to press against the pad, - a sheathing housing being arranged on the head of the piston having housing walls and a first opening suitable to directly face the cylinder and a second opening suitable to directly face the braking pad; - a sheathing body developing from an inner diameter (Di) to an outer diameter (De) and defining an axial direction (I-I), a radial direction orthogonal to the axial direction and a circumferential direction; said sheathing body comprising: - a first hooking ring being arranged along the outer diameter (De) of the sheathing which projects in the axial direction and is suitable to be fixed to a caliper body; - a second hooking ring being arranged along the inner diameter (Di) of the sheathing; - a sheathing portion (Pg) which extends from said inner diameter (Di); - said body comprises a joining band, said joining band extending substantially in a planar manner in the radial direction in the shape of a disc; - the joining band extends in the radial direction by a predefined second extension or radial extension of joining band; - said second hooking ring projects in the axial direction and is suitable to be fixed to the piston; - the sheathing comprises a plurality of folds separated from said second hooking ring and made up by folds being defined by portions of said sheathing body that are folded such as to have the surfaces thereof directly facing each other and such as to allow the extension of the sheathing during the outward movement of the piston from the cylinder of the caliper body; said plurality of folds being totally arranged on said sheathing portion (Pg) extending from the inner diameter (Di); - said joining band connects the first hooking ring to the plurality of folds; - the plurality of folds extends in the radial direction by a predetermined first extension or radial extension of folds; - said sheathing housing of the piston entirely accommodates said plurality of folds of the sheathing, thereby avoiding that a housing for the plurality of folds should be provided within the caliper body