The main problems in structural analysis by Finite Eelement Method are difficulty in making data file and error estimation. For decreasing these problems' pays. have been suggesting the adaptive mesh refinement and error estimation method. Posteriory error estimation methods suggested by Jang[1], Babuska[2,3], Ohtsubo[8,9], and this paper. Comparing these methods and examine their properties. According this paper, In the problem supposed having singularity, the method suggested by this paper is good, But the problem supposed having no singularity, the method suggested by Jang[1] is good. For decreasing the effect of initial mesh in p-refinement, make application h-refinement at first and apply p-refinement, and confine polynomial's degree to two, for making program simply by plural mesh models are not needed.