This article describes a procedure for the calculation of the intermodulation behavior of the TM010 mode in high temperature superconducting (HTS) disk resonators from a description of the local HTS nonlinearities. Successful cross-checks are performed by comparing the theoretical results with experimental measurements and simulations based on the multiport harmonic balance algorithm for a specific model of HTS nonlinearity. The application of this procedure to the determination of nonlinear material parameters from disk resonator measurements is illustrated and compared to theoretical predictions.