A method of constructing one or more buildings each having a reticular structure, of the type comprising emplacement "in situ" of plural constructed storey modules attached to vertical columns (1, 2, 3, 4) of the reticular structure by means of bolting, welding, or riveting, wherein it comprises the stages of: - erecting a set of the vertical columns (1, 2, 3, 4) forming a vertical load-bearing structure, on foundations or piles; - arranging, at a lower part of the structure, a pile of the plural constructed storey modules, within the space defined by the columns (1, 2, 3, 4), and in a same vertical order as a definitive order foreseen for each of the storey modules of the structure forming a building amongst the one or more buildings; - hoisting the plural storey modules by means of an elevation system until each storey module is positioned in a definitive emplacement at a corresponding height within the space defined by the columns (1, 2, 3, 4); and - attaching each of the storey modules to the columns (1, 2, 3, 4) by means of bolting, welding, or riveting; characterized in that the stage of attaching the storey modules includes the resting of the modules on brackets solidary to the columns (1, 2, 3, 4), said brackets being articulated in order to open with the passage of the storey module and to spring back once the storey module has passed, activated by a number of return springs. emplacement "in situ" of plural constructed storey modules attached to vertical columns (1, 2, 3, 4) of the reticular structure by means of bolting, welding, or riveting, wherein it comprises the stages of: - erecting a set of the vertical columns (1, 2, 3, 4) forming a vertical load-bearing structure, on foundations or piles; - arranging, at a lower part of the structure, a pile of the plural constructed storey modules, within the space defined by the columns (1, 2, 3, 4), and in a same vertical order as a definitive order foreseen for each of the storey modules of the structure forming a building amongst the one or more buildings; - hoisting the plural storey modules by means of an elevation system until each storey module is positioned in a definitive emplacement at a corresponding height within the space defined by the columns (1, 2, 3, 4); and - attaching each of the storey modules to the columns (1, 2, 3, 4) by means of bolting, welding, or riveting; - erecting a set of the vertical columns (1, 2, 3, 4) forming a vertical load-bearing structure, on foundations or piles; - arranging, at a lower part of the structure, a pile of the plural constructed storey modules, within the space defined by the columns (1, 2, 3, 4), and in a same vertical order as a definitive order foreseen for each of the storey modules of the structure forming a building amongst the one or more buildings; - hoisting the plural storey modules by means of an elevation system until each storey module is positioned in a definitive emplacement at a corresponding height within the space defined by the columns (1, 2, 3, 4); and - attaching each of the storey modules to the columns (1, 2, 3, 4) by means of bolting, welding, or riveting; characterized in that the stage of attaching the storey modules includes the resting of the modules on brackets solidary to the columns (1, 2, 3, 4), said brackets being articulated in order to open with the passage of the storey module and to spring back once the storey module has passed, activated by a number of return springs.