In this work, the Method of Lines applied to the study of the propagation caracteristics of planar structures is presented. In this method, the spacial variables are discretized in several lines orientated in a direction normal to the conductor strips. Then, the partial differential equations are reduced to ordinary differential equations having well known solutions. Although this method uses finite differences, it is much more efficient with respect to computer speed and memory necessary, in comparison to the conventional finite difference method. A few planar structures with three dieletric layers, inside rectangular waveguides were analysed, and the results are compared with those using other reported methods. In the appendix, it is shown how to develop computer programs using non-uniform discretization for the improvement of the efficiency of this method. Also, the discretization in two directions is presented, which is adequate for analysis of microwave resonators. This work is intended as a basic approach to hel in further analysis using the Method of Lines.