In the previous report, the authors proposed a simple adaptive mesh refinement technique for the elastoplastic finite-element analysis, where an element is refined when the absorbed energy density reaches a prescribed value during the loading procedure. Though the method gave accurate solutions when the prescribed value for mesh refinement was not very large, the solutions were not accurate when the prescribed value was so large that the material yielded. In the present report, several algorithms are added to the original one to overcome this problem. The additional algorithms are summarized as follows, (1) If interpolated stresses of the elements newly created by refinement exceed the yield surface, the stress components are reduced to the yield surface. (2) When the material yields, the method proposed by Owen and Hinton is employed in order to prevent the stresses drifting away from the initial yield surface. (3) The effective stress at a node is employed as a criterion for mesh refinement in addition to the absorbed energy density. Through numerical examples, it is shown that the modified algorithm gives accurate solutions. Secondly, the algorithm is applied to large-deformation problems. Consequently, it is shown that a more precise solution is obtained effectively by the present method compared with the solution obtained by the initial mesh subdivision.