Although estimation of a stress distribution in a soil mass assumed as an anisotropic medium gives more realistic results but it is impractical since many elastic parameters are required to be measured. Possibility of more practical way of estimation of a stress distribution, including cross-anisotropy in a different and simpler manner is investigated in this research. In this study a new anisotropic parameter, s, was presented into the theoretical deduction. To see the performance of the proposed method, five independent cross-anisotropic elastic parameters such as E-V, E-H, V-VH, V-HH, G(VH) and anisotropic parameter, s, of a clayey soil were measured and stress distributions under the center of uniformly distributed circular area were portrayed for the same soil. In this frame, Finite Element Method (with cross-anisotropic linear elastic material model), the proposed method, Boussinesq and Westergaard solutions were carried out and results were compared. It is found that the stresses obtained by the proposed way are compatible with the other solutions and also the stresses agreed with that of FEM analysis beneath a certain depth.