Fiber reinforced plastic (FRP) jacketing has emerged as an effective way to retrofit concrete columns in recent years. The existing experimental work on FRP confined concrete column is mainly concentrated on concrete columns under concentric loading. Therefore, this research involves the study of nonlinear finite element 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 effects of the FRP layer number, concrete compressive strength, percentage of main steel, rectangularity of columns and various ratios of lateral loads to centric load on FRP confined concrete columns were investigated theoretically. The results of this work were compared with previous work [1] 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 “NL”. The FEM results indicated that R.C. columns externally wrapped with CFRP sheet showed a significant improvement in both capacity and ductility.