The design, construction and testing of deep superconducting magnetic traps for neutral atoms and molecules were studied. The support structure was designed to be simple in order to avoid unforeseen stress concentrations which led to catastrophic mechanical failure. Optical access to the trapping region along the axial direction was provided by the 76.5 mm bore of the magnet. The results show that the magnet temperatures much below 4.2 K necessitate the use of a different material for the support structure in the applications which required the magnet to be run at low currents.