Resonant power absorption is an important phenomenon during microwave heating. The resonances that occur when plane electromagnetic waves are incident on infinitely long cylinders and slabs are investigated as a function of sample dimensions. For cylinders two kinds of incident waves are studied: TMz when the electric field is oriented along the axis of the cylinder and TEz when the magnetic field is oriented along the axis. At a resonant condition the overage power absorbed by the sample is a local maximum. Due to attenuation within the sample the resonances decrease in intensity as the sample size increases. Using the dielectric properties of water, resonances are found to be a function of the ratio of the sample dimension to the wavelength of radiation, λs, in the sample. For slabs of thickness L and integer values of n, resonances occurred at L/λs = 0.5n; for cylinders of diameter D, resonances occurred at D/λs = 0.5n – 0.257. The generality of these relations to predict resonances in other food samples are shown using existing dielectric data. Resonances in cylinders for both polarizations occurred at similar radii. However, the radius at which the first resonance occurred for the TMz case was absent in the TEz case.