By the variational method, the coplanar waveguide(C.P.W) shielded by two conducting plates has been analyzed. The particular potential solution has been obtained for the boundary conditions in C.P.W. The characteristic impedance and the effective dielectric constant in C.P.W. have been obtained by the variational method using the potential function and the assumed basis function for charge distributions. To consider the effect of the conducting plate in C.P.W. two cases, with and without the top plate, have been analyzed and compared respectively.