The aim of this study is to develop a new approach for analyzing the influence of various factors on the distribution of contact pressure and the shape of the contact area between complex-profile bodies. This need arises from the increasing use of components with intricate geometries in modern mechanical systems. These complex-profile bodies facilitate the transfer of motion trajectories and dynamic forces or momentum. Both are determined by the initial gap between the bodies that cannot generally be described accurately using a quadratic form of the coordinates of the tangent plane. Additionally, the surfaces of the contacting bodies may include material layers that are not adequately represented by traditional Winkler-type models. The proposed approach is based on a modification of the Kalker’s variational principle. The formulation can include arbitrary geometry of the contact surfaces and incorporate various types of mechanical behavior of the intermediate surface layers. Both factors affect the distribution of the contact pressure and the shape of the contact area, which is illustrated by several representative examples. Various nontrivial shapes of the contact area other than elliptic are retrieved, including dumbbell-shaped and multiply connected domains with various localizations of maximum contact pressure. These findings are crucial for the rational design of new mechanisms and machines that involve contact between complex-profile components.