Abstract: An intensifier pump has a primary fluid cylinder including a primary piston and which has shaft portions received within a separate coaxial fluid chamber. A secondary fluid cylinder having a secondary piston has shaft portions reciprocally received within a separate coaxial fluid chamber. The secondary piston is of a smaller relative diameter than the primary piston. The sizing of the hydraulic pistons in the operating fluid cylinders is used to sequence the pistons in the cylinders with the largest diameter piston being stroked first followed by the second largest diameter cylinder being stroked next, followed in turn by any additional fluid cylinders in the order of the piston diameter size. When the smallest diameter cylinder has been stroked, a pressure switch signals a reverse flow pump to change the direction of circulation of the operating fluid to cycle the pistons.