This thesis develops a mechanistic model of glucose metabolism in the human body, representing transport and oxidization of glucose to maintain energy balance. The model is a set of differential equations. The forms of these equations are primarily based on qualitative understanding of the relevant physiological process and the related chemical reactions and experimental data. The parameters in these differential equations represent physiological characteristics and therefore have physical meanings. The first part of this thesis develops a model of glucose metabolism, which includes the brain, the liver, skeletal muscle and the pancreas. The model is mechanistic because it includes, among other things, detailed representations of glucose transporters and the metabolic pathways. The transporters have different properties in different organs. The parameters in the model come from chemical balances, ranges of normal values published in the literature, curve fitting of experimental data and tuning. In simulation protocols of meals and various exercise intensities, the results demonstrate a qualitative agreement with the dynamics of glucose metabolism in healthy subjects. The next part of this thesis develops a sub-model of the pancreas which includes more differential equations representing additional physiological processes. The parameters of this pancreas model are obtained by a global optimization method. Parallel computing is implemented to handle the large computational cost of the optimization method. The simulation results demonstrate that this pancreas model can capture the transient response in intravenous glucose tolerance tests (IVGTT), which is an important characteristic of a healthy pancreas. The values of the parameters can categorize subjects such as normal ones, as well as mild, moderate and treated type 2 diabetics. Unlike much of the literature, the model is validated by comparison to experimental results that are not used in the parameters identification process. The sub-model of glucose transport in skeletal muscle is also refined to incorporate more physiological information. Its parameters are also obtained by the optimization method. The simulation results demonstrate varied rates of glucose transport into muscle under different exercise intensities.