A platform support device (1A, 1B) for lifting loads or people along a structure, in particular to perform work applied to said structure, this device including: - at least one platform (1A, 1B), with vertical movement, - modular elements (4, 6), able to be assembled to reach a desired height, forming, in the assembled state, at least two vertical masts (16, 17), the modular elements conforming the mast body and the modular element conforming the mast head, - lifting elements (2, 3) of the platform of the winch type able to connect the platform to the modular head elements of the masts, to adjust, as desired, the elevation level of the platform (1A, 1B) along the masts, these lifting elements of the winch type being able to be disconnected from said masts at will, - means for temporarily immobilizing the platform (1A, 1B) relative to a modular element of each mast (16, 17), to allow, in the immobilized state of the platform (1A, 1B), the addition or removal, at the head of the masts, of at least one modular mast element as a function of the desired elevation height of the platform (1A, 1B), the placement of each mast element (4, 6) being done from the platform (1A, 1B), the or each platform (1A, 1B) being placed between two independent modular masts (16, 17) forming an elevation and guide path, the masts (16, 17) being positioned on either side of the ends of the platform, characterized in that each mast (16, 17) includes at least four uprights connected to one another by spacers, inclined or horizontal, the pairs of uprights constituting guide paths, in that each mast (16, 17) has at least two guide paths (11, 12), for the parallel lifting of two platforms, arranging a free surface between them for connecting means to connect the mast to the structure along which each mast is positioned, without detriment to the upward and downward movement of the platform(s) (1A, 1B) along said masts, said surface being free of any stress during the movement of the platform(s) (1A, 1B) along the mast, i.e., free for means connecting the mast to the structure, in that the or each platform (1A, 1B) cooperates with a guide path (11, 12) for each mast so as in particular to allow - either a same mast to be used for the parallel lifting, synchronously or asynchronously, of two platforms (1A, 1B), - or, after lateral shift of a mast, to re-create a lifting path using a single mast by cooperation with the mast having remained in place and in that each platform (1A, 1B) is guided in rolling contact along the masts (16, 17), said means for guiding a platform (1A, 1B) along a mast being made up of rollers, preferably with a groove, supported by a support able to be separably coupled to the platform (1A, 1B), these rollers rolling along a pair of uprights of the mast. - at least one platform (1A, 1B), with vertical movement, - modular elements (4, 6), able to be assembled to reach a desired height, forming, in the assembled state, at least two vertical masts (16, 17), the modular elements conforming the mast body and the modular element conforming the mast head, - lifting elements (2, 3) of the platform of the winch type able to connect the platform to the modular head elements of the masts, to adjust, as desired, the elevation level of the platform (1A, 1B) along the masts, these lifting elements of the winch type being able to be disconnected from said masts at will, - means for temporarily immobilizing the platform (1A, 1B) relative to a modular element of each mast (16, 17), to allow, in the immobilized state of the platform (1A, 1B), the addition or removal, at the head of the masts, of at least one modular mast element as a function of the desired elevation height of the platform (1A, 1B), the placement of each mast element (4, 6) being done from the platform (1A, 1B), - either a same mast to be used for the parallel lifting, synchronously or asynchronously, of two platforms (1A, 1B), - or, after lateral shift of a mast, to re-create a lifting path using a single mast by cooperation with the mast having remained in place