The design of an axial flow compressor stage has been formulated as a nonlinear mathematical programming problem with the objective of minimizing the aerodynamic losses and the weight of the stage, while maximizing the compressor stall margin. Aerodynamic as well as mechanical constraints are considered in the problem formulation. A method of evaluating the objective function and constraints of the problem with a pitchline analysis is presented. The optimization problem is solved by using the penalty function method in which the Davidon-Fletcher-Powell variable metric minimization technique is employed. Designs involving the optimization of efficiency, weight of the stage, and stall margin are presented and the results discussed with particular reference to a multivariable objective function.