A two State lattice model of soluble proteins is extended td model membrane proteins. The relationship between the structure of model proteins and their sequences is investigated as a function of the relative energy of hydrophobic type interactions. Relative energies of the interactions of hydrophobic and hydrophilic subunits with the solvent, the membrane, and with one another were chosen to mimic, within the simple model, their experimental counterparts. It is found that this reasonable energy parameterization produces model membrane proteins which share many characteristics with real membrane proteins, while other parameter sets fail in this regard. Consideration of the results obtained with the reasonable parameter sets leads to predictions about membrane proteins. Among these are that a single sequence may give a proteinlike native state in both aqueous and membrane environments.