A computing model is constructed describing spectrum and energy characteristics of two-dimensional Open Resonators (OR) that contain various types of inhomo-geneities (dielectric, ideally conducting, resonance, etc.). This model is based on the spectral theory of analytical operator functions in the Hilbert space and on the procedure of quasi-inversion of the operators corresponding to the initial boundary value problems. A number of numerical experiments were carried out, using a computer to study the physical features of spectrum characteristics of inhomogeneous OR, aimed at their implementation in devices of the mm wave range. Wavelengths, geometrical parameters of OR mirrors and their mutual arrangements, and inhomogeneity dimensions were varied in a broad range. In particular, the wave dimensions of the inhomogeneous OR were such that for their analysis the known quasi-optical OR models are inapplicable.