A mixed finite element formulation for analyzing the propagation characteristics of lossy or dissipative waveguides is presented. Maxwell's equations are expressed in terms of the transverse electric and magnetic field components. This formulation is discretized using this mixed finite element and the classical Lagrange's one. A comparison of these discretizations shows that the use of this mixed finite element eliminates the spurious modes. This method is applied to computing the propagation characteristics of a MIS microstrip line.