In this work, the coplanar stripline (CPS) and its discontinuities: open-end, short-end, gaps and resonator have been modeled. New integral equations for the electrical field components are formulated, in the spectral domain, using an exact dyadic Green's function, applied to the CPS structure. The use of this form of Green's function allows the consideration of the effects of the dielectric losses, the surface wave excitation and the space wave radiation on the propagation characteristics of the CPS and its discontinuities. The resulting integral equation has been solved using the two-dimensional Galerkin's technique. The resolution of the resulting matrix equation gives the scattering parameters of the studied structures. The obtained results are commented and compared with those of other approaches and measurements.