Wave-propagation properties of microstrip transmission lines can be determined accurately if an exact electrostatic-field solution can be found for a pair of charged conductors separated by a dielectric sheet. The latter problem is framed as an integral equation for whose solution simple numerical methods are available. To determine the kernel function of this integral equation, the classical method of images is generalised to include, multiple partial images; the kernel function is then given by well convergent infinite series. Wave impedances calculated using this theory yield very good agreement with experiment. Detailed results are given for the propagation velocity in microstrip lines with very thin strip conductors, and the method used to solve thick-strip problems is described.