Abstract: A hydraulic fluid-driven, multicylinder, modular, reciprocating piston pumping machine of non pulsating flow and independently variable forward and return stroke speeds comprises several pumping modules (A, B . . . E) each having one primary cylinder (A1, B1 . . . E1) and one secondary cylinder (A2, B2 . . . E2) coaxially joined by an angularly and radially oscillating bushing (100) through which slides a piston rod (A3, B3 . . . E3) with an angularly oscillating piston (A4, B4 . . . E4; A5, B5 . . . E5) at each of its ends. Each primary cylinder (A1, B1 . . . E1) has the end opposed to the bushing closed by valve monifolds (A11, B11 . . . E11) interconnected through a pressurized hydraulic fluid distritubor conduit (5) through which pressurized hydraulic fluid is supplied to the primary cylinder of each module by at least one hydraulic pump (1, 2). A hydraulic fluid chamber (A18, B18 . . .