The coupled electromagnetic wave equations and energy balance equations are solved via Galerkin finite element method with Crank-Nicholson time integration scheme to numerically simulate the microwave heating of model lossy samples enclosed in various low (alumina) and high (SiC) lossy containers. The primary objective of this work is to identify the alteration of heating or power absorption characteristics of the lossy sample in the presence of containers and analyze the role of container thickness. Microwave propagation is modeled via Helmholtz equations, which are the time-harmonic representation of Maxwell equations. The scattering at the air-material interface is efficiently modeled via an integro-differential radiation boundary condition. Power absorption and temperature distribution are evaluated for a range of container thicknesses and sample dimensions representing thin sample with uniform power absorption, intermediate sample with resonating power absorption and thick sample with exponentially attenuated power absorption. For each case, simulations are also carried out in the absence of the containers. It is found that the power absorption and temperature distribution are strongly influenced by both the low (alumina) and high (SiC) lossy containers. Overall, power absorption and/or heating quality can be greatly enhanced in the presence of alumina containers. SiC containers suppress power absorption within the sample. However, SiC containers lead to more controlled and uniform heating. Thickness of the container is found to be the critical factor for enhanced power absorption or heating quality of the sample.