Abstract: The present invention includes an assembly and method to pump fluids produced by a drilled well within a geological formation having a borehole wall fixed by casing. The invention includes a subsurface pump having a stationary member and a mobile member. A pump anchor fixes the pump to the well casing. A hollow continuous tube or coiled tubing extends within the well bore from the surface down to the lower portion of the well bore. The bottom end of the coiled tubing is connected to the mobile member of the pump. Preferably, the coiled tubing can be coiled and uncoiled from a reel located on the surface. A hollow polished rod has a bottom end coupled to a free top end of the coiled tubing. The hollow polished rod is connected to means to operate the hollow rod according to a selected movement, preferably reciprocating axial movement. The pumped fluids are recovered on the surface from the hollow polished rod and coiled tubing.