The use of composite materials in the fabrication of optical telescope mirrors offers many advantages over conventional methods, including lightweight, portability and the potential for lower manufacturing costs. In the construction of the substrate for these mirrors, sandwich construction offers the advantage of even lower weight and higher stiffness. Generally, an aluminum or Nomex honeycomb core is used in composite applications requiring sandwich construction. However, the use of a composite core offers the potential for increased stiffness and strength, low thermal distortion compatible with that of the facesheets, the absence of galvanic corrosion and the ability to readily modify the core properties. In order to design, analyze and optimize these mirrors, knowledge of the mechanical properties of the core is essential. In this paper, the mechanical properties of a composite triangular cell core (often referred to as isogrid) are determined using finite element analysis of a representative unit cell. The core studied offers many advantages over conventional cores including increased thermal and dimensional stability, as well as low weight. Results are provided for the engineering elastic moduli of cores made of high stiffness composite material as a function of the ply layup and cell size. Finally, in order to illustrate the use of these properties in a typical application, a 1.4-m diameter composite mirror is analyzed using the finite element method, and the resulting stiffness and natural frequencies are presented.