The purpose of this series of studies is to develop finite element computer models of the mechanical properties of cellular polymers, especially open cell foams. Using finite element methods, both the properties of the material making up the struts, as well as the geometrical structure of the cell, can be readily varied. The series of studies begins with two-dimensional hexagonal honeycombs because of their ease of analysis and comparison with previous works. Comparison of the present solutions and analytic ones have been conducted, and excellent agreement is obtained. The effects of cell dimensions, such as strut length, strut depth, and cell height, of irregular hexagons on the effective Young’s modulus of foams were studied in the low strain and elastic regime. Load direction and cell geometry anisotropy effects are also investigated. In addition, the effects of friction model and the specimen size on the effective Young’s modulus of the foam are studied. Nonuniform strut thickness was also a variable. The modulus effects of these variations in geometry ranged from minimal to highly significant and provide an understanding of geometry effects on foam performance.