The process of finite element analysis that deals with large deformation often produces distorted elements in the later stages of the analysis. These distorted elements lead to analysis problems, such as inaccurate solutions, slow convergence, and premature termination of the analysis. This paper proposes a new mesh generation algorithm to mesh the input part for pure Lagrangian analysis, where our goal is to improve the shape quality of the elements along the analysis process to reduce the number of inverted elements at the later stage, and to decrease the possibility of premature termination of the analysis. One pre-analysis is required to collect geometric and stress information in the analysis. The proposed method then uses the deformed-shape boundary known from the pre-analysis, finds the optimal node locations, considers the stress information to control the mesh sizes, as well as control the mesh directionality, generates meshes on the deformed boundary, and finally, maps the elements back to the undeformed boundary using inverse bilinear mapping. The proposed method has been tested on two forging example problems. The results indicate that the method can improve the shape quality of the elements at the later stage of the analysis, and consequently extend the life of the analysis, thereby reducing the chance of premature analysis termination.