Computational　methods　for　additional　stresses　in　foundations　are　an　important　topic　in　soil　mechanics.　This　paper　develops　a　new　numerical　method　for　additional　elastic　fields　in　layered　and　non-homogeneous　foundations.　The　techniques　adopted　primarily　involve　the　use　of　a　two-dimensional　integration　to　integrate　the　fundamental　solutions　of　a　transversely　isotropic　and　layered　halfspace　under　point　loads　over　the　distributed　pressure.　To　analyze　non-uniform　loads　over　an　arbitrary　area,　the　loading　area　needs　to　be　discretized　into　a　finite　number　of　quadrilateral　elements.　The　regular　and　singular　integrals　in　the　expressions　of　elastic　fields　in　foundations　are　accurately　calculated.　Numerical　examples　show　that　the　proposed　method　can　provide　highly　accurate　results　and　can　be　used　to　analyze　the　foundations　with　the　elastic　parameters　arbitrarily　varying　with　depth.　The　proposed　method　is　explicitly　and　concisely　expressed　for　effective　teaching　and　learning.　©　2024　Chinese　Academy　of　Mechanics.　All　rights　reserved.