Computer simulations of lipid bilayers and biological membranes using molecular mechanics calculations have been undertaken in order to study these complex systems which are so vital in the control and functioning of many biological processes. The preliminary research involved the development of a model that recreates experimentally observed properties. This is not a trivial task since structural data on lipids in the biologically relevant liquid crystalline phase are unavailable precisely because of their fluid nature. The starting configuration designed for simulation of lipids in the fluid phase contained four different lipid conformations. These reflected the most probable head group and glycerol moiety conformations plus gauche dihedrals were introduced into the hydrocarbon chains so that they resembled chains in the fluid phase and reduced the time required for equilibration molecular dynamics. The bilayer model was then used to study cholesterol-lipid and peptide-lipid interactions. The cholesterol simulations illustrated how this molecule orders lipid chains by virtue of its rigid skeleton while the peptide simulations showed how cooperative the interactions between proteins and lipids are. Finally simulations of ion channels of gramicidin and melittin in membranes were accomplished and conclusions drawn on the nature and mechanism of the toxicity of melittin and of how water and ion translocation occurs along gramicidin channels.