Abstract: Numerical calculation of the elastic engineering constants of unidirectional fibre composites based on an effective medium theory (EMT)⁴ is here employed to find the Young's modulus of 2-dimensional as well as 3-dimensional randomly oriented fibre composites by a method of geometrical average over orientations due to Christensen & Waals³.The results compare faverably with similar calculations based on theories of Halpin-Tsai⁸ and Christensen⁷,and show good conformity with experimental data.Thus it is shown that EMT is applicable to the calculation of elastic properties of randomly oriented fibre composites.