This work investigates the effect of acrylic and glass containers on microwave heating of a representative low lossy dielectric material enclosed in the container and exposed to uniform plane microwaves from one side. Microwave heating characteristics are determined via detailed mathematical models for the electric field and temperature distributions within the semi-infinite sample–container assembly. An in-house FORTRAN based algorithm involving Galerkin finite element method is developed to solve the governing equations and determine the heating characteristics (power and temperature distributions) for various sample dimensions as a function of container thickness. It has been found that the acrylic container can be safely used without any significant alteration of the heating characteristics of the dielectric samples. On the other hand, the glass container can lead to a significant alteration of the heating characteristics as a function of container thickness. The power absorption, heating pattern (location of the heating fronts) and spatial heating uniformity within dielectric samples are found to vary significantly with the thickness of the glass container. The results indicate that the glass container can play the critical role to alter the heating characteristics based on the processing requirement (uniform heating or targeted heating at varying locations). These results are expected to play important roles for material processing and the role of the glass containers towards optimal microwave processing applications is revealed for the first time. These results are also important for further investigations on the containers (materials, shapes etc.) and their potential applications for the enhanced, controlled or targeted microwave processing of materials. © 2022 Elsevier Ltd