We present measurements of the low-temperature thermal conductivity of a number of polymeric and composite materials from 0.3 to 4 K. The materials measured are Vespel SP-1, Vespel SP-22, unfilled PEEK, 30% carbon fiber-filled PEEK, 30% glass-filled PEEK, carbon fiber Graphlite composite rod, Torlon 4301, G-10/FR-4 fiberglass, pultruded fiberglass composite, Macor ceramic, and graphite rod. These materials have moderate to high elastic moduli making them useful for thermallyisolating structural supports.