Method for producing a three-dimensional object which comprises a plurality of supports that are connected to the body of said object by means of joining elements in each one of which it is possible to identify a shaped area, recessed with respect to the external surface of said joining element and having a bottom corner that delimits a pre-established fracture area for the detachment of said support, wherein each one of said joining elements comprises a first body projecting from the external surface that delimits the body of said object and a second body projecting from said support, said first and said second body (8, 9) having the external surface that is curved and convex and being connected to each other in such a way as to define said shaped area whose bottom corner delimits said pre-established fracture area by means of a stereolithography process, including the computer graphic design of the joining elements of the supports to its body comprising the following operations: - designing the body of said three-dimensional object and a plurality of supports; - designing a plurality of first elements, each defined by at least one centre and one convex curved external surface; - intersecting said first elements with the body of said three-dimensional object in such a way as to define for each one of said first elements a portion projecting from the body of said three-dimensional object; - designing at one end of each one of said supports a second element defined at least by one centre and by one convex curved external surface; - applying to the centre (80c, 90c) of each one of said elements (80, 90) the versor (80v, 90v) that defines its convex curved external surface (80s, 90s); - aligning with each other said versors (80v, 90v) of each pair of said elements (80, 90); - intersecting said second element with said portion of said first element projecting from the body of said three-dimensional object; - defining the values of the distances (X1, X4; Y1, Y2, Y3) of said centres (80c, 90c) of said elements (80, 90) from each other and with respect to the external surface of the body of said three-dimensional object; - designing said elements (80, 90) and said supports in the configurations reached according to said defined values of the distances so as to define said shaped area whose bottom corner delimits said pre-established fracture area. - designing the body of said three-dimensional object and a plurality of supports; - designing a plurality of first elements, each defined by at least one centre and one convex curved external surface; - intersecting said first elements with the body of said three-dimensional object in such a way as to define for each one of said first elements a portion projecting from the body of said three-dimensional object; - designing at one end of each one of said supports a second element defined at least by one centre and by one convex curved external surface; - applying to the centre (80c, 90c) of each one of said elements (80, 90) the versor (80v, 90v) that defines its convex curved external surface (80s, 90s); - aligning with each other said versors (80v, 90v) of each pair of said elements (80, 90); - intersecting said second element with said portion of said first element projecting from the body of said three-dimensional object; - defining the values of the distances (X1, X4; Y1, Y2, Y3) of said centres (80c, 90c) of said elements (80, 90) from each other and with respect to the external surface of the body of said three-dimensional object; - designing said elements (80, 90) and said supports in the configurations reached according to said defined values of the distances so as to define said shaped area whose bottom corner delimits said pre-established fracture area.