A method of inflating, in alternating manner, inflatable cells of a support device for supporting an element to be supported is provided, which device is of the mattress type for supporting the body of a patient, said mattress being made up of cells that are inflatable with a fluid, in particular air, and having at least one zone made up of first and second series of inflatable cells referred to respectively as “first” cells and as “second” cells, the cells of each series communicating fluidly with one another and with inflation means, in which method alternating deflation and re-inflation cycles are performed during which each of said series of cells is deflated and then re-inflated in alternation and in succession, said first cells being deflated and then re-inflated simultaneously respectively with the re-inflation and with the deflation of said second cells, the alternating deflation and re-inflation of said first and second cells of the support device taking place in a cycle controlled by said inflation means being switched on/off, wherein the switching on/off of said inflation means is controlled as a function of the values of the pressures of the fluid measured inside said cells and of comparison of said values with at least one reference pressure value determined as a function of the morphology of the patient.