Lunar-based astronomy requires structures that provide the required stiffness, strength, and dimensional stability in the challenging lunar vacuum, thermal, radiation, micrometeorite, secondary ejecta, and dust environments. Materials used in the structures must be durable to provide extended service life. They must not outgas and thereby interfere with optics. Structures must function as part of an integrated system involving detectors, metrology, and optics. The thermal environment of the lunar surface is particularly taxing because the long-duration exposures to extremes of temperature. Designers must cope with transient thermal gradients associated with passing from sunlight to darkness and back to sunlight. Also, the shape of mirrors and other components at night-time low temperatures may differ from shape at day-time high temperatures because of material properties varying significantly over the range from about 70 K to nearly 400 K. Materials for structural components include several types of glass, metals and their alloys (e.g., aluminum, beryllium, and titanium), graphite epoxy and the associated class of materials, and metal matrix composites (e.g., graphite magnesium and graphite aluminum). Examples of material properties are presented. Structural design concepts for several possible observatories are presented. Structural configurations will be partially determined by the need to reduce direct human involvement in the construction process. Concepts discussed include the 16-meter optical/ultraviolet telescope and a small telescope with 0.8-m aperture intended to be landed on the Moon by a robotic spacecraft. For lunar-based astronomy, structures must rest on the lunar regolith with loads transferred to the regolith through a foundation. The overall response of the structure is dependent on the interaction of the foundation and the regolith.