An analysis has been carried out using conformal transformation for the case of a symmetric stripline filled with multilayered discrete dielectric media with their interfaces parallel to the ground planes. This has been applied to a stripline structure filled with a medium having a relative dielectric constant which is continuously varying in a direction perpendicular to the ground planes. Eight different distributions, such as Gaussian, parabolic, and semicircular, are considered for this variation of relative dielectric constant. Impedance data on stripline are preseuted for all these cases. The results of limiting cases obtained from this general formulation are compared with those existing in the literature.