A pump system/method configured to provide substantially constant flow of concrete, cement, or other material is disclosed. The system integrates a trapezoidal cutting ring and spectacle plate in conjunction with lofted transitional interfaces to the hydraulic pump cylinder rams and output ejection port to ensure that pressurized discharge concrete material is not allowed to be relaxed nor backflow into the material sourcing hopper. The trapezoidal cutting ring is configured to completely seal off the trapezoidal spectacle ports as it smoothly transitions between the hydraulic pump input ports during cycle changes thus generating a more uniform output flow of concrete while eliminating hopper backflow and hydraulic fluid shock. A control system is configured to coordinate operation of the hydraulic pump cylinder rams and cutting ring to ensure that output ejection port pressure and material flow is maintained at a relatively constant level throughout all portions of the pumping cycle.