A new method for systematically constructing basis functions for two-dimensional field problems containing a strip conductor buried in stratified dielectrics is proposed. By applying a simplifying averaging process to the associated static problem, the structure of the specific kernel or Green's function for the problem can be determined approximately. An integral form of continuity equation is derived; general sets of quasi-eigenfunctions are established, which are orthogonal and complete in Hubert spaces L2(Ω, w). By substituting the specific information into the latter, the required quasi-eigenfunctions for the problem can be obtained. Hence, with both the edge condition and the continuity equation being satisfied simultaneously and with the inhomogeneity of dielectric constants being taken into account, these resultant functions form a particularly suitable expansion basis for the series solution to such physical quantities as scalar potential, induced surface charge, and surface current.