The batch chemical reaction is chosen as the process model to be optimized and the rate constants are functions of pressure only, as the reactions are assumed to occur isothermally. The time optimal control problem considered here means to determine the minimum time path from the given initial compositions to desired final compositions by manipulating the process pressure. A gradient method or a steepest-ascent method is applied to determine the control variable program by using the high speed digital computer. Numerical solutions are presented for the following three cases: (1) no constraint on the operating pressure ...... open and matched terminal constraint. (2) constraint on the operating pressure ...... open terminal constraint. (3) constant operating pressure ...... open terminal constraint.