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The objective of this study is to establish design criteria for contained phase-change material (PCM), thermal-energy storage modules located within a tank through which a heat transfer fluid flows. The scope required to meet the objective includes (1) review of the existing research in latent heat thermal energy storage, (2) development of mathematical models for contained PCM thermal energy storage systems, (3) model validation, (4) parametric studies using the models to establish key parameters in the design of such systems, and (5) evaluation.and comparison of various system designs. In this report the emphasis will be on phase change containers which have a rectangular geometry. The mathematical formulation and numerical results are based on one-dimensional conduction heat transfer for a cartesian coordinate system. The formulation and results for spherically shaped containers arranged in a packed bed can be found in the thesis by Timmer [1]. Although significant differences do exist between the formulations for the rectangular and spherical geometries, conceptually the two are identical. Thus, each formulation and the results following from that formulation are presented in separate reports in an effort to enhance clarity.