We present a spherical microwave discharge model, which takes into account the higher modes of the incident electromagnetic waves. The discharge model is constructed on the basis of the channel approximation of the LTE plasma. Numerical experiments are carried out for the discharge in an argon at atmospheric pressure. Results are presented for the characteristics of the discharge plasma against the external parameters (the size of the discharge chamber and the applied electromagnetic field mode, power and frequency). (c) 2005 WILEY-VCH Verlag GmbH W Co. KGaA, Weinheim.