The existing experimental work on FRP confined concrete column is mainly concentrated on concrete columns under co centric loading in recent years. Therefore this research involves the study of nonlinear FE analysis of FRP confined square and rectangular R.C. columns under both axial compressive and lateral loads. Lateral load was taken as a ratio of the axial compressive loads "H/ Pc". The results of this work were compared with previous work (Soghair, H.M. et al. 2004) considered the behavior of square and rectangular columns confined with CFRP under centric loads. All studied columns were modeled using the nonlinear finite element analysis. The main variables studied were the cross-section shape of the column "R", concrete grade "C", the percentage of area of the main longitudinal steel "As%" and the number of layers of CFRP sheet "NE'. The FEM results indicated that R.C. columns externally wrapped with CFRP sheet showed a significant improvement in both capacity and ductility.