Microwave thawing of materials, which melt over a finite temperature range, are analyzed using the effective heat capacity method. The state of the material, solid, liquid or mush is deduced from the equilibrium liquid volume fraction vs. temperature relationship for the substance, and the microwave power is calculated from Maxwell’s equations. Using Galerkin finite elements, the microwave power temperature and liquid volume fractions were obtained for microwave thawing of tylose slabs. Thawing progresses from the inside and/or outside depending on the slab thickness. For slabs greater than or equal to 5 cm, thawing progresses predominantly from the surface of the sample. Resonances, during which the microwave power absorption is high, causes the 2-cm slab to thaw quicker than 1-cm slabs. A power law for the thawing time vs. sample thickness yields an exponent of 1.56 for microwave thawing and 2 for conventional thawing. To control the temperature rise in the liquid regions, simulations were carried out with an on-off control on the microwave power. On-off control results in greater power savings for thick samples.