Resonances or maxima in power absorption due to microwaves incidence within a slab are analyzed via transmitted and reflected waves. A generalized mathematical formulation for uniform plane waves has been established to analyze traveling waves, stationary waves and microwave power absorption within a multiphase sample. Preliminary studies based on the generalized mathematical analysis in ice and water slabs illustrate that greater amplitudes of traveling and stationary waves occur within ice samples, whereas, greater intensity of spatial resonances in microwave power occurs for water samples due to a greater dielectric loss of water. Microwave thawing is studied for specific sample thicknesses which are selected based on greater power distribution within water samples. The enthalpy method is employed for modeling of thawing of ice samples where a superficial mushy region is assumed around the melting point. Depending on the sample thickness, thawing may occur from the unexposed face as well as both the faces when the sample is exposed to microwaves at one face only, whereas thawing may originate from both the center as well as the faces when the sample is exposed to microwaves at both faces. Our analysis based on the generalized mathematical formulation validates the local maxima in spatial power distribution during intermediate thawing stages obtained with the finite element based enthalpy formulation. The generalized mathematical analysis on multiple thawed regimes further illustrates the role of traveling waves on resonances in microwave power. The influence of resonance is attributed by a non-monotonic variation of thawing time with sample thicknesses either for one side incidence or both side incidence due to microwaves. Optimal thawing strategies are recommended based on greater power savings. (C) 2003 Elsevier Ltd. All rights reserved.