The use of an elliptical Gaussian beam (EGB) for applications relying on light scattering depends much on the ability to evaluate the beam shape coefficients (BSC) effectively and accurately. Based on the angular spectrum decomposition (ASD) of the radial components of the beam field, we present the formulations of the BSCs for the EGB. Numerical calculations of the BSCs, the beam reconstruction, and light scattering are performed. The fidelity of the reconstructed field to the given one is discussed so as to examine the BSC calculation. A comparison of the ASD method with the quadrature and localized approximation methods leads to the conclusion that the ASD method is much faster than the quadrature method, and it is very powerful for acquiring reliable and accurate results of BSCs, even for far off-axis locations and high ellipticities of the EGB.