Abstract: By using the continued-fraction solution and introducing auxiliary variables, the dynamic sti ness and mass matrices of bounded domains are expressed in high-order matrices. The formulation is based on an improved continuedfraction solution of the scaled boundary finite element equation in dynamic sti ness. This continued-fraction solution converges over the whole frequency range with increasing order of expansion. Compared to the original approach, it leads to numerically more robust for large-scale systems and arbitrarily high orders of expansion. The eigenvalue problem of a regular octagon is considered. Transient analysis of a bounded rectangular plane is also presented. The results of two numerical examples demonstrate that the proposed method is superior to the original approach and it is suitable for dynamic analysis of large-scale systems.