A fully compensating uranium-scintillator calorimeter was constructed for the ZEUS detector at HERA. Several of the barrel calorimeter modules were subjected to beam tests at Fermilab before shipping them to DESY for installation. The calibrations of the modules used beams of electrons and hadrons, measuring the uniformity of the response, and checking the resolution. The runs also provided opportunity to test a large fraction of the actual ZEUS calorimeter readout system in an integrated beam environment more than one year before HERA turn on. The experiment utilized two computer controlled mechanical structures. one of which was capable of holding up to four modules in order to study shower containment, and a magnetic spectrometer with a ...