Abstract: After analyzing the coefficient matrices of periodic structures resulted from the finite element method(FEM), a FEM with partial assemblage was put forward. Some block iteration processes, such as BSOR and BCG/BPCG, were employed to solve the linear algebraic equation. The Lanczos algorithm for treating large eigenvalue problems was then modified by these iteration procedures. The endeavor makes it possible to avoid direct treatment with large scale matrices during the static and dynamic analyses of periodic structures. Examples show that the above work dramatically reduces the necessary incore and outcore space of computers.