Abstract: The analytical method for stress of foundation under vertical load is an important basis of design and computation in foundation engineering. However, the existing methods cannot reflect the properties of granular media for foundation soils. Therefore, according to the current researches on stress transmission of granular media, firstly, supposing that the stress in a granular medium foundation under vertical point load always diffuses downward with a curve cone, an analytical problem for the stress of the granular medium foundation under vertical point load is converted into that of a curve cone under vertical point load at its top, and a stress-solving method for a curve cone is obtained by discussing the stress-solving method for a line cone, hence, an analytical method for the stress of the granular medium foundation under vertical point load is proposed. Then, an analytical method for the stress of the granular medium foundation under circular vertical uniform load is established by regarding the problem as the integral solution of the stress of the granular medium foundation under vertical point load, which can adequately report the characteristics of the granular media of foundation soils and shows obvious superiority to the Boussinesq solution. Finally, by simultaneously adopting the proposed analytical method and Boussinesq solution as well as the numerical analytical method with PFC^3D, a comparative analysis of stress distribution in granular medium foundation under circular vertical uniform load is carried out, and it is indicated that the proposed method is reasonable and feasible.