A modular device for clamping and/or supporting a workpiece on a base plate of a machine tool, the device comprising - a main body with a central cavity defining a longitudinal axis and having a first longitudinal end portion and a second longitudinal end portion, said second end portion having an external thread; - first fixing means comprising a pin adapted to be introduced into said first end portion of said body and to be secured to the workpiece; - a ring nut mounted outside said main body and having an internal thread which is screwed onto said external thread of said second end portion; - a plurality of locking members adapted to be introduced into corresponding angularly offset seats of said main body and each having an outer end adapted to cooperate with the inner surface of said ring nut for receiving a radial thrust therefrom; wherein said pin comprises, proximate to one of its longitudinal ends, an annular recess designed to cooperate with the locking members; characterized by comprising second fixing means which are adapted to be introduced into said second end portion and to be secured to the base plate, said annular recess having a first conical contact surface, said locking members having an inner end with a first portion having a concave shape complementary to that of said first conical contact surface to exert a uniform clamping force thereon, with an axial component. - a main body with a central cavity defining a longitudinal axis and having a first longitudinal end portion and a second longitudinal end portion, said second end portion having an external thread; - first fixing means comprising a pin adapted to be introduced into said first end portion of said body and to be secured to the workpiece; - a ring nut mounted outside said main body and having an internal thread which is screwed onto said external thread of said second end portion; - a plurality of locking members adapted to be introduced into corresponding angularly offset seats of said main body and each having an outer end adapted to cooperate with the inner surface of said ring nut for receiving a radial thrust therefrom; wherein said pin comprises, proximate to one of its longitudinal ends, an annular recess designed to cooperate with the locking members; characterized by comprising second fixing means which are adapted to be introduced into said second end portion and to be secured to the base plate, said annular recess having a first conical contact surface, said locking members having an inner end with a first portion having a concave shape complementary to that of said first conical contact surface to exert a uniform clamping force thereon, with an axial component. wherein said pin comprises, proximate to one of its longitudinal ends, an annular recess designed to cooperate with the locking members; characterized by comprising second fixing means which are adapted to be introduced into said second end portion and to be secured to the base plate, said annular recess having a first conical contact surface, said locking members having an inner end with a first portion having a concave shape complementary to that of said first conical contact surface to exert a uniform clamping force thereon, with an axial component.