本文採用Hill的異向性降伏理論及Updated Lagrangian Formulation (ULF)的觀念，建立一增量型彈塑性大變形三維有限元素分析程式，以模擬方杯深引伸成形製程。並利用流線法及其補正公式預測固定杯高之初始料片外形，根據不同杯高的假設來預測各料片之初始輪廓，再進行方杯深引伸成形分析，進而判斷出方杯深引伸成形極限之最佳化初始料片之輪廓曲線。本文並設計一組方形模具，進行方杯深引伸成形實驗，並與數值分析所得之工件杯高與厚度分佈作比較，進而得到最佳化初始料片之方杯深引伸成形極限，此數值分析所得之結果均可合理的預測實驗成果。 A methodology for formulating an elasto-plastic finite element model was developed to analyze the deep drawing process of the square cup. The model was based on the Updated Lagrangian Formulation and Hill’s yield criterion. The stream line method with the compensated formulation was used to predict the initial profile of the blank under the condition of the fixed cup height. With the different assumption of the cup height, the prediction of the optimum contour profile would be achieved. Also, the simulation of the deep drawing of square cup was proceeded to determine the initial contour profile of optimal blank to the forming limit. A set of tools was designed to perform the deep drawing experiment of the square cup. A good agreement is obtained from the comparison of results between the simulation and experiment, such as the distribution of cup height and the distribution of the workpiece thickness. In addition, the forming limit can be gained from the deep drawing experiment of the optimum blank of the square cup. Therefore, the simulation result can reasonably predict the experiment result.