Abstract-A model for the two-dimensional analysis of microstrip lines, named Rigorously Coupled Multi-conductor Strip (RCMS) is introduced. In this model, the width of the strip of a microstrip line is subdivided into a large number of rigorously coupled narrow strips. So, a microstrip line can be considered as a coupled multi-conductor transmission line. Determination of the capacitance and inductance matrices of the model is introduced, also. The voltages and currents induced by electromagnetic fields for the coupled multi-condutor strips problem can be obtained using Bernardi's method. The effect of an external EM wave on a microstrip line with non-uniformity in its width is computed by adding the circuit model of transverse discontinuity (narrow slit) to the RCMS model. Finally, the validity and efficiency of the introduced method is investigated using previous work and full wave EM-simulation software.