A falling head support device for supporting beams of formworks for floors, comprising: - an upright, which can be fixed at its end to a supporting strut that rests on the ground, - a supporting head for at least one beam for supporting a form work for floors, which is coupled so that it can slide along said upright, said supporting head being provided with safety abutment elements for the end of the supporting beam during the setup and removal of the formwork of said supporting beam, - means for reversibly locking said supporting head in a preset position defined along said upright, said supporting head comprising: - two plates, which are arranged mirror-symmetrically so that they are laterally adjacent to opposite sides of said upright and are suitable to delimit laterally a region for accommodating the end of the at least one supporting beam, - at least two recesses for guiding the insertion and containment of a supporting portion of the corresponding supporting beam, each recess being provided on a respective one of said plates, the bottom of each recess forming at least part of the supporting surface of the supporting portion of the supporting beam, - a transverse element for connecting said two plates, which is suitable to support temporarily an inclined lower portion of the supporting beam during the setup and removal of the formwork of said beam characterized in that said recesses have a substantially V-shaped profile and guide the insertion and containment of said supporting portion of the corresponding supporting beam, which is constituted by the lower portion of an inverted T-shaped body formed at the end of said supporting beam, and said safety abutment elements for the end of the supporting beam during the setup and removal of the formwork of said beam are constituted by hook-shaped portions, which protrude outward, as a continuation of the upper portions of said recesses, toward the upper region of said plates, the concave region of said hook-shaped portions being substantially directed toward said upright. - an upright, which can be fixed at its end to a supporting strut that rests on the ground, - a supporting head for at least one beam for supporting a form work for floors, which is coupled so that it can slide along said upright, said supporting head being provided with safety abutment elements for the end of the supporting beam during the setup and removal of the formwork of said supporting beam, - means for reversibly locking said supporting head in a preset position defined along said upright, - two plates, which are arranged mirror-symmetrically so that they are laterally adjacent to opposite sides of said upright and are suitable to delimit laterally a region for accommodating the end of the at least one supporting beam, - at least two recesses for guiding the insertion and containment of a supporting portion of the corresponding supporting beam, each recess being provided on a respective one of said plates, the bottom of each recess forming at least part of the supporting surface of the supporting portion of the supporting beam, - a transverse element for connecting said two plates, which is suitable to support temporarily an inclined lower portion of the supporting beam during the setup and removal of the formwork of said beam characterized in that said recesses have a substantially V-shaped profile and guide the insertion and containment of said supporting portion of the corresponding supporting beam, which is constituted by the lower portion of an inverted T-shaped body formed at the end of said supporting beam, and said safety abutment elements for the end of the supporting beam during the setup and removal of the formwork of said beam are constituted by hook-shaped portions, which protrude outward, as a continuation of the upper portions of said recesses, toward the upper region of said plates, the concave region of said hook-shaped portions being substantially directed toward said upright.