A flexible pipe for conducting fluid, such as offshore production fluids, has interior tubing, a series of rings and clamps, and exterior tubing. The interior tubing has an extruded tube and a surrounding layer. Outer rings dispose about the interior tubing and abut end-to-end. Inner rings dispose on the tubing and fit in between each of the outer rings. These inner rings have tapered surfaces that fit against beveled ends defined in each end of the outer ring's internal bore. The clamps affix the abutting ends of the outer rings together, and the exterior tubing disposes on the series of rings and clamps. This exterior tubing has an inner layer of wrapped tape surrounded by an extruded tube. A flange couples by an end clamp to the end ring of the pipe, and inner and outer supports on the flange support the interior and exterior tubing.