Abstarct: This research work is devoted to the formulation of nonlinear elastic problems baxsed on the isogeometric analysis method. For this purpose, a summary of the particle kinetics is reviewed and the related equilibrium equations are presented. Then, the formulation of hyperelastic materials is explained and the equilibrium equations are derived and linearized for the use of the iterative Newton-Raphson method. Since the isogeometric analysis method is employed for analysis, its basics are pointed and the discretization of unknown functions and geometry in hyperelasticity by using the NURBS basis functions and the control variables are explained. An algorithm for analysis of this category of problems is proposed and the obtained hyperelasticity results by the isogeometric analysis method are compared with finite elements. In the continuation, the effects of the number of Gauss integration points, the number of load increments, the different strain energy functions and different incompressible material on the convergence of the solution are discussed.