Abstract: Process for assembly of an electric pump, comprising the following phases: (a) a pump proper (1) is formed including a pump body (2) provided with an induction orifice (3), a delivery orifice (4) and electrical terminals (5, 6) to supply it with energy; (b) a cage (7) is arranged around the said pump body (2); (c) a filtering element (15) is fixed to one of the ends of the said pump body (2) by connecting it to the said cage (7) so that the said induction orifice (3) communicates with the said filtering element (15); and (d) the assembly thus obtained is introduced into a pump casing (17) and they are connected one to the other; characterised in that, after phase (c) and before phase (d), a tubular vibration damping element (16) is arranged on the said cage (7), the said tubular element (16) also forming a sole connection organ between the said cage (7) and the said pump casing (17).