Sandwich construction incorporating a honeycomb cellular core offers the attainment of structures that are very stiff and strong in bending while the weight is kept at a minimum. Generally, an aluminum or Nomex honeycomb core is used in applications requiring sandwich construction with fiber-reinforced composite facesheets. However, the use of a fiber-reinforced composite core offers the potential for even lower weight, 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 to suit specialized needs. Furthermore, the material of the core itself will exhibit anisotropic material properties in this case. In order to design, analyze and optimize these structures, knowledge of the effective mechanical properties of the core is essential. In this paper, the effective three-dimensional mechanical properties of a composite hexagonal cell core are determined using a numerical method based on a finite element analysis of a representative unit cell. In particular, the geometry of the simplest repeating unit of the core as well as the appropriate loading and boundary conditions that must be applied is presented.