The objective of this study is to evaluate the effects of size and permittivity on the specific absorption rate(SAR) values of rat brains during microwave exposure at mobile phone frequency bands. A finite difference time domain (FDTD) technique with perfect matching layer(PML) absorbing boundaries is used for this evaluation process. A color coded digital image of the Sprague Dawley(SD) rat based on magnetic resonance imaging(MRI) is used in FDTD calculation with appropriate permittivity values corresponding to different tissues for 3, 4, 7, and 10 week old rats. This study is comprised of three major parts. First, the rat model structure is scaled uniformly, i.e., the rat size is increased without change in permittivity. The simulated SAR values are compared with other experimental and numerical results. Second, the effect of permittivity on SAR values is examined by simulating the microwave exposure on rat brains with various permittivity values for a fixed rat size. Finally, the SAR distributions in depth, and the brain-averaged SAR and brain 1 voxel peak SAR values are computed during the microwave exposure on a rat model structure when both size and permittivity have varied corresponding to different ages ranging from 3 to 10 weeks. At 900 MHz, the simulation results show that the brain-averaged SAR values decreased by about 54 % for size variation from the 3 week to the 10 week-old rat model, while the SAR values decreased only by about 16 % for permittivity variation. It is found that the brain averaged SAR values decreased by about 63 % when the variations in size and permittivity are taken together. At 1,800 MHz, the brain-averaged SAR value is decreased by 200 % for size variation, 9.7 % for permittivity variation, and 207 % for both size and permittivity variations.