In this paper, we present a full-wave analysis of microstrip lines printed on variable thickness substrates using the method of lines (MoL). The propagation constant of a microstrip line in the interface of one dielectric is computed as a function of different shape characteristics. The results are compared with those obtained in previous research, especially with those using the discrete mode matching technique (DMM). Good agreement is found between the results. Furthermore, the convergence behavior of the method of lines is examined and finally, we show some numerical results, obtained with analyzing this structure in a large band of frequencies.