Abstract: In this paper, the complicated lengthy Mindlin stress formulas are rearranged and simplified, new formulas of the Mindlin stress distributions under various load conditions are presented. By making the additional stress coefficients dimensionless, the stress coefficient formulas under some loading conditions are derived. These coefficients are expressed in terms of the ratio of foundation length to its width, the ratio of depth to foundation width, the ratio of foundation's embedded depth to its width (or radius), and the Poissons ratio. The prerequisite's when the Mindlin's formula can be replaced by the Boussinesq's formula, the scope of the tensile stress of the Mindlin solution and its effect on the foundation settlement, the effect of the Poissons ratio in the Mindlin's formula on the stresses, the discrepancy between the theoretical prediction of settlement results and on-site observation value are discussed in detail.