Hertzian theory includes a well-known analytical solution for the calculation of the contact area and pressure between two bodies. Hertzian theory is not unconditionally applicable, in particular with regards to the shape of the contacting solids. When geometric assumptions are invalid, the finite element method is generally used, but is more computationally intensive. We propose and analyze a generalization to the geometric assumptions of Hertzian theory and apply it to torus on plane contacts. In order to evaluate the accuracy of the calculation, a finite element model is used as a basis for comparison.