The simulated anneal procedure based on the Metropolis Monte Carlo algorithm is presented as a new numerical method for the analysis of electron-spin-resonance spectra by the spin Hamiltonian formalism. It gives an alternative way for finding the global minimum of a function, which describes the difference for each of the resonance fields between the theoretically calculated energy difference and the experimentally measured microwave energy. Compared to the iterative procedures commonly used, it has the advantage of not getting stuck in local minima of the parameter space. This implies that the procedure can be started with arbitrary initial parameters. The usefulness of the method is illustrated by its application to the analysis of four defects in alkali halides doped with heavy metal ions. © 1986.