The Echellette Spectrograph and Imager (ESI) is one of several second-generation instruments for the Keck telescopes. The motivation for the f/15 Cassegrain-mounted instrument has been to provide a versatile, extremely efficient, and stable system for faint object spectroscopy and imaging, on a comparatively limited schedule and budget. In keeping with these goals, a space-frame instrument structure has been designed, analyzed, and fabricated. The mainframe structure provides the mechanical interface between the telescope and instrument, support points for all the optical, mechanical, and electronic sub-systems, and provides a rigid base for the active- collimator flexure control system. The fundamental concepts and motivation for using a space-frame are discussed, and their application to the design, analysis, and fabrication of the ESI structure is presented.