Composite axisymmetric shells have numerous applications; many researchers have taken advantage of the general shell element or the semi-analytical formulation to analyze these structures. The present study is devoted to the nonlinear analysis of composite axisymmetric shells by using a 1D three nodded axisymmetric shell element. Both low and higher-order shear deformations are included in the formulation. The displacement field is considered to be nonlinear function of the nodal rotations. This assumption eliminates the restriction of small rotations between two successive increments. Both Total Lagrangian Formulation and Generalized Displacement Control Method are employed for analyzing the shells. Several numerical tests are performed to corroborate the accuracy and efficiency of the suggested approach.