In this paper the resonant modes of a radio frequency industrial heating applicator system are determined numerically. This is carried out using a finite element eigenvalue calculation of the electric field of the system. Both the complex linear and nonlinear forms of the generalized large sparse eigenproblem are solved, the latter being obligatory when material properties are frequency-dependent. The basis is the Implicity Restarted Arnoldi/Lanczos Methods which can be used to calculate the multiple resonant modes occurring in the operating frequency range of interest. Once the resonant modes of a specific system have been obtained, an electric equivalent circuit model can be derived. The numerical results presented are compared to experimental measurements carried out on a prototype experimental system showing good agreement.