The modes of a shielded microstrip transmission line are determined by a variational method which is also suitable for the analysis of multiple strips and lines embedded in multiple dielectric layers. For the case of an asymmetric strip the modes are compared with experimental results and orthogonality of the modes is tested by direct numerical computation. It is shown that the variation in phase constant `β' with the degree of asymmetry can be controlled with a dielectric overlay. Consequently, circuit tracks can be placed close to the box walls and the variation in β ignored. The power flow and hence the characteristic impedance `Z0' may also be determined for the dielectric overlay using expressions for the electric and magnetic fields in the layers of the transmission line which may be easily determined by considering the TE and TM equivalent circuits.