The multipinch experimental device was constructed to study the stability and plasma confinement properties of a reversed-field pinch (RFP) with a magnetic well. The magnetic well is created by shaping an RFP configuration into two equal-current lobes in which the poloidal field cancels at the X point of a figure-eight-shaped magnetic separatrix. The design and construction of a 0.525-m major radius modular machine to study this unique plasma configuration is described. A novel construction technique for the noncircular cross-section plasma chamber, incorporating a thin metal skin, phenolic honeycomb, and graphite/epoxy composite bonded sandwich structure, is discussed. Details of the fabrication of the vacuum liner, conducting shell, the toroidal and poloidal coil systems, and the iron core are given.