In the last three decades, the research in flexible multibody dynamics has made substantial progress, in particular, the nonlinear finite element represented by the Absolute Nodal Coordinate Fromulation (ANCF) has been widely applied to deal with the system of flexible multibody dynamics. However, in this formulation the slope vectors are selected as the element node coordinate, the increased scale of the freedoms for the complex structures gives rise to the computational burden. Based on the above issues, the beam and shell elements described with Non-Uniform Rational B-Splines (NURBS) curves and surfaces have been proposed in the frame of Isogeometrical Analysis (IGA). Based on the total lagrangian formulation, the deformation of the elements is described with the Green strain, and the strain energy of the elements can be obtained. Besides, the elastic force and its Jacobian matrix of the elements are also deduced. Finally, four case studies including both static and dynamic problems are given to validate the proposed beam and shell elements. High efficient and accurate formulation has been proposed in the research of flexible multibody dynamics.