Portable pump (11) for infusing liquid substances into the body of a living being, said pump being provided with a casing (13) which receives electromechanical members comprising a power supply unit (15), an electronic control unit (17), an electric motor (19), an assembly (21) for converting the rotary motion of an output shaft (23) of the motor (19) into a linear sliding motion of a pusher (25) axially moveable for causing the movement of a plunger (35a) slideable within an interchangeable reservoir (35), open at one end (35c) thereof, in which the substance to be infused through the pump is contained and which is accommodated in a housing (33) inside the casing (13), wherein the housing (33) is in communication with the outside through an opening (37) which is formed in one of the casing walls and through which the reservoir (35) can be inserted into and removed from the housing and from which an appendix (35b) of the reservoir protrudes for the exit of the substance to be infused when the reservoir is accommodated in the housing, wherein the housing for the interchangeable reservoir includes, with respect to the opening (37), a distal portion (33a) provided with mechanical means for reversible engagement (39) for the reservoir end (35c) opposite to the appendix (35b) and a proximal portion (33b) provided with an annular sealing gasket (41) which surrounds the reservoir (35) and forms a tight seal between the reservoir (35) and the casing (13) wall when the reservoir is mechanically engaged within the housing (33) through said engagement means (39), so that when the reservoir (35) is mechanically secured within the housing (33) through the engagement means (39), the tight seal between the reservoir (35) and the casing (13) wall is simultaneously guaranteed.