Novel and accurate global and local surface impedance models have been developed to analyze plasmonic circuits fast and efficiently. In the analysis procedure, first the metal strip in the plasmonic circuit is modeled by a surface impedance. Then, the calculated surface impedance is employed in the surface integral equation to analyze the plasmonic circuit such as a through line and line coupler. Accuracy of the numerical results is shown in comparison with a commercial simulation software. The number of unknowns as well as the computational time are also compared with the volume integral equation, and it is obvious that, using our proposed surface impedance models, the analysis will be much faster and more efficient. This could have been evident from the beginning because usage of the surface impedance model helps bring the unknowns to the boundary of the structure, which reduces the number of unknowns.