Estimation of differential settlements for large steel storage tanks is a very important design consideration; however, there is a lack of readily available analysis tools which can be used to accurately and conveniently compute tank differential settlements under various bottom plate dimensions and soil stiffnesses. This paper presents a continuum-based, elastic analysis model for a uniformly loaded, circular tank foundation resting on soil. The analysis captures the three-dimensional nature of the soil-structure interactions and produces settlement profiles of the tank foundation and the surrounding soil. The soil is assumed to behave as a linear-elastic material in a semi-infinite half space, and the foundation is modeled as a circular plate with a finite thickness. The governing differential equations are derived based on energy principles and calculus of variations. Input parameters for the analysis model are the plate diameter, plate thickness and elastic constants of the soil and plate. Model validation includes comparing results from this study with those from the literature and from finite element analyses, and these comparisons show good agreement. Parametric studies are then carried out to investigate the effects of plate diameter, plate thickness, and soil stiffness on differential settlement between the center and the edge of the circular plate. Based on the results from the parametric studies, design charts for use in preliminary design of circular tank foundations are proposed to estimate the differential settlement for given soil properties and plate geometry.