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In this thesis, the results of a series of computer stimulation studies into the thermodynamics and the kinetics of biological membranes and permeation processes are presented. The first chapter contains a brief overview of the project and its aim, and the second introduces the techniques of molecular dynamics computer simulations. In chapter 3, the biological background of cell membranes is presented and experimental techniques to study properties of pure lipid bilayers are described. Previous simulation studies are also reviewed. The membrane computer model is the subject of chapter 4, containing the simulation protocol and results. Membrane physical properties as they result from simulations are compared with available experimental data to validate the computer model proposed and the latter is shown to be physically realistic. Chapter 5 describes how permeability coefficients across lipid bilayers and cell monolayers can be measured in experiments. A technique which allows for the permeability coefficients to be obtained from molecular dynamics simulations is also described in detail. In chapter 6, the latter technique is employed to study the permeation of small organic solutes across the membrane computer model previously described and is validated by comparison with experimental data, which are available for most of the chosen small molecules. This yields new insights into the mechanism of membrane permeation. Chapter 7 describes the choice, the parameterization and the conformational study of candidate drug molecules, for which permeability coefficients across the membrane model are calculated in chapter 8 with the same methodology used for the small organic solutes in chapter 6. Results are compared with permeability coefficients through Caco-2 cells, which are commonly employed to measure the ability of drugs to permeate human tissues, and help to elucidate the process of drug absorption after administration. The final chapter contains conclusions and future work. The appendix reports the parameters developed and employed for simulating the drug molecules.