This article presents a new numerical absorbing boundary condition useful for quasi-TEM analysis of open-type microwave transmission lines employing the finite-element method (FEM). The standard FEM equations are used for the inner nodes of the mesh, and mesh truncation is achieved by imposing linear relationships for the nodes on the outer boundary and their neighbors, which are derived from the appropriate Green's functions. This approach greatly reduces the mesh size, while preserving the sparsity of the FEM equations. Higher-order approximations of the absorbing boundary condition are derived through the use of higher-order-finite elements. (C) 1995 John Wiley & Sons, Inc.