This paper examines the design aspects and numerical modeling of single- and multi-mode, high power, microwave resonant cavity applicators. A novel numerical electromagnetic modeling approach, based on the finite difference solution of Maxwell's equations in the time domain, is utilized taking into account the finite conductivity and thickness of the cavity walls. Results obtained from the model enable an unambiguous choice of the optimum iris size for critical coupling; shape, dimension, orientation and number of radiating elements for a prescribed irradiation pattern of slotted waveguide feeds as well as dimensions and excitation mechanism of multimode cavities. The model also allows the evaluation of the volumetric distribution of the microwave energy at any point inside the load and may eventually be used to determine the dynamic transient temperature profiles induced during the curing process.