The uncertainty that prevails in the financial and investment environment has prompted banks to seek out greater efficiency in the management of their assets and liabilities. Today's asset management decisions create tomorrow's problems as well as opportunities. This need has led banks to determine their optimal balance among profitability, risk, liquidity and other uncertainties. The optimal balance between these factors cannot be found without considering important interactions that exist between the structure of a bank's liabilities and capital and the composition of its assets. In managing its assets and liabilities, a bank should face several conflicting goals, such as the maximization of returns, the minimization of risk, the maintenance of a desirable level of liquidity and solvency, the expansion of deposits and loans. The present paper describes a linear goal programming model for asset liability management and apply it to data from a commercial bank of Greece. Taking into account all the above we include the essential institutional, legal, financial, structural and bank-related policy constraints as proposed from the bank's board.