A caliper body for a brake caliper for a disc brake, adapted to be arranged straddling a brake disc, said brake disc comprising a first brake disc braking surface and an opposite second brake disc braking surface, said disc brake defining an axial direction (X-X), either coinciding with or parallel to the brake disc rotation axis, a radial direction (R-R), orthogonal to the axial direction (X-X), and a circumferential direction (C-C), orthogonal both to the axial direction (X-X) and to the radial direction (R-R); said brake caliper comprising: - a wheel side first elongated element, comprising a first elongated element caliper outer side and a first elongated element caliper inner side, wherein said first elongated element caliper outer side is adapted to face a vehicle wheel and wherein said first elongated element caliper inner side is adapted to face said first brake disc braking surface, either directly or indirectly, by means of at least one first pad; - an opposite wheel side second elongated element, comprising a second elongated element caliper outer side and a second elongated element caliper inner side, wherein said second elongated element caliper inner side is adapted to face said second brake disc braking surface, either directly or indirectly, by means of a second opposite pad; - at least one first caliper bridge, which connects said wheel side first elongated element and said opposite wheel side second elongated element, so as to be adapted to straddle said brake disc; wherein a middle plane (M-M) orthogonal to the axial direction (X-X) and interposed between said first elongated element caliper inner side and said second elongated element caliper inner side, said middle line (M-M) defining an axial outer sense (XE-XE) directed in axial direction (X-X) from said middle plane (M-M); and wherein a radially outer sense (RE-RE) is defined directed in radial direction (R-R) from the rotation axis of the brake disc; and wherein: - at least either said wheel side first elongated element or said opposite wheel side second elongated element comprises at least one thrust means housing adapted to receive thrust means, adapted to actuate the first pad against said brake disc first braking surface or the second opposite pad against said second opposite brake disc braking surface; - said at least one thrust means housing is substantially cup-shaped and comprises a housing bottom wall and a housing lead-in portion, axially opposite to said housing bottom wall, - said housing lead-in portion comprises at least one housing edge surface, adapted to face a back of a support plate of a pad (14 or 16) which can be associated with the caliper body; and wherein: - at least either said first elongated element caliper inner side or said second elongated element caliper inner side comprises at least one groove bottom wall and groove sides which delimit at least one groove, wherein said at least one groove bottom wall is axially outer with respect to said housing edge surface; characterized in that - said at least one groove comprises at least one first groove mouth, or radially outer groove mouth, and at least one opposite second groove mouth, or radially inner groove mouth, at the opposite end of the longitudinal path of said groove. - a wheel side first elongated element, comprising a first elongated element caliper outer side and a first elongated element caliper inner side, wherein said first elongated element caliper outer side is adapted to face a vehicle wheel and wherein said first elongated element caliper inner side is adapted to face said first brake disc braking surface, either directly or indirectly, by means of at least one first pad; - an opposite wheel side second elongated element, comprising a second elongated element caliper outer side and a second elongated element caliper inner side, wherein said second elongated element caliper inner side is adapted to face said second brake disc braking surface, either directly or indirectly, by means of a second opposite pad; - at least one first caliper bridge, which connects said wheel side first elongated element and said opposite wheel side second elongated element, so as to be adapted to straddle said brake disc; - at least either said wheel side first elongated element or said opposite wheel side second elongated element comprises at least one thrust means housing adapted to receive thrust means, adapted to actuate the first pad against said brake disc first braking surface or the second opposite pad against said second opposite brake disc braking surface; - said at least one thrust means housing is substantially cup-shaped and comprises a housing bottom wall and a housing lead-in portion, axially opposite to said housing bottom wall, - said housing lead-in portion comprises at least one housing edge surface, adapted to face a back of a support plate of a pad (14 or 16) which can be associated with the caliper body; - at least either said first elongated element caliper inner side or said second elongated element caliper inner side comprises at least one groove bottom wall and groove sides which delimit at least one groove, wherein said at least one groove bottom wall is axially outer with respect to said housing edge surface; characterized in that - said at least one groove comprises at least one first groove mouth, or radially outer groove mouth, and at least one opposite second groove mouth, or radially inner groove mouth, at the opposite end of the longitudinal path of said groove.