1. The elastomeric infusion pump assembly comprising: a central core with a substantially cylindrical body having a first end and an opposite second end, a length, a substantially constant outer diameter defining a first radius (R), the central channel extending across the length of the rod, the first port being between the first end and the second end and extending from the outer diameter to the center channel with the passageway for providing a fluid fill port disposed at the first end and communicating with said channel, and yhodnoy port located at the second end and in communication with said channel irastyagivaemuyu elastomeric tube disposed around the central shaft between its first and second ends and coaxial to it, with the overlap of the first port, wherein the tube is sealingly attached to the central shaft near its ends and has an original inner diameter defining a second radius (r), corresponding to the first radius (R), a length (L), which is less than the length of the central shaft, and a thickness (t) wall selected from the conditions (0,4225 × r)