In this study container structures such as cylindrical vessels which have a flat or shallow spherical shell bottom on a Vlasov foundation with variable soil characteristics, are investigated. The variation of the soil's elastic modulus is assumed exponential along the depth of soil layer. Interaction between superstructure, foundation and soil is taken into account. The loading is considered as axisymmetric relative to the center of the bottom. The solution is achieved using the flexibility method, in which the wall is represented by distributed loads and moments along the circumference of the bottom. Some parametrical results are obtained for various soil layer depth-to-bottom radius ratios and comparisons are made between exponential and the other variations of the soil's elastic modulus.