Abstarct: In recent years, using of fiber reinforced polymer (FRP) is one of the most application methods for strengthening RC members as columns. In compressive members, FRP jacket was wrapped around the columns and with confining the concrete causes the enhancement in axial load-carrying capacity of them. Original attempt of this thesis, is modeling of non-linear behaviour of confined concrete by ANSYS software. For modeling non-linear behaviour of concrete, Drucker-Prager criteria that is the improved of Mohr-Coulomb criteria were used. To validate the proposed FE models, the test results obtained from other researchers were compared with the models results and very good agreement was found. In this research, at first confining improvement of FRP jacket by shape modification of column’s cross section of rectangular RC columns has been studied. In this method of column’s strengthening, before wrapping the column, its cross section by implementation of concrete cover modified to circular or elliptical cross section and then the column has wrapped. This modification causes more uniform distribution of confining pressure of FRP jacket. The results show that the effect of shape modification of column is the most efficient and economical way for improving of confinement. Of course, architectural limitations, limit the using of this method. Then, the eccentricity effects of loading on the load-carrying capacity of rectangular RC columns were evaluated. In following of this study, interaction diagrams of axial load and bending moment for the columns obtained from finite element and proposed method of ACI 440.2R-08 were compared. Models results indicated that with the eccentricity nevertheless small, load-carrying capacity of confined column will greatly reduce. With increasing eccentricity, the effectiveness of confinement has decreased, so that in tensioned controlled zone, particularly in the pure bending point, confinement of column is very, very little. Also comparing of these two types of diagrams, indicates that in the compression-controlled zone, the results of ACI is conservative, however results of Ver. 2008 of this design guideline, comparing with its Ver. 2002 is more realistic.