An ultrahigh pressure pump includes a frame including at least one radially-extending member having an outer frame pivot disposed at outer end thereof; a crank rotatably mounted in the frame and adapted to be driven by a power source and a crank pin offset from a rotational axis of the crank; and at least one radially-extending telescoping pump subassembly having inner and outer ends. The outer end of each pump subassembly is attached to the outer frame pivot for pivotal swinging movement thereabout, and the inner end is pivotally attached to the crank pin. The pump subassembly operates substantially free from side loads on the piston rod and has a long component life.