Abstract: The absolute nodal coordinate method has been widely usedto study the dynamics of flexible multibody systems. The computationalefficiency of this method, however, has much room to be improved. Generally,the second kind of Piola-Kirchhoff stress tensor is used to derive theelastic forces and corresponding Jacobians, namely, the partial derivativematrix of the elastic forces with respect to the generalized coordinates.Nevertheless, this method is inefficient enough. Based on the principle ofvirtual work, the analytical formulations for the elastic forces and theirJacobians are deducted directly by using the first kind of Piola-Kirchhoffstress tensor. Numerical example results based on different methods showthat the proposed approach is able to enhance the computational efficiencysignificantly.