Leakage inductance is a critical design element of a transformer in a galvanically isolated power converter. For multi-objective optimization-based designs of power converters, analytical leakage inductance models that are computationally efficient and accurate are preferred over the finite element methods (FEMs). In this article, three new analytical models are proposed - triple-2-D, double-2-D, and single-2-D - that are formulated using the magnetic image method. These 2-D models are used to calculate the leakage inductance of a partially filled shell-type transformer having a circular center leg, and the resulting errors are less than 1.25% for each model when compared to the 3-D FEM simulated value of the leakage inductance. Additionally, three different conductor models are considered, and their relative accuracies and computational efficiencies are investigated. Furthermore, a variable inductance transformer (VIT) is designed, whose leakage inductance can be modified by moving one of the windings vertically along the central core leg. The analytically evaluated variable leakage inductances of the VIT are in good agreement with the 3-D FEM simulated and experimentally measured values.