The formal description of the assets and liabilities management (ALM) by a bank within regulatory requirements leads to an optimal control problem with phase constraints. The phase constraints arise from the restrictions on banking activities, which are set by law to maintain the banking process. Solving such model explicitly is rarely possible, and numerical calculations enable to study its properties. The indirect method of the solution involves formulating the system of necessary optimality conditions and then computation of the ordinary differential equations system combined with specific equations for dual variables. This paper provides the details of application of the numerical methods and its specifics in the proposed economic model.