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A novel surface impedance model is developed to analyze plasmonic circuits supporting long range surface plasmon polaritons (LR-SPP). The analysis is carried out in two steps. First, a higher order approximation of the surface impedance is obtained for the metal strip through a 2-D analysis of the waveguide cross section. Second, the developed surface impedance boundary condition is incorporated in the mixed potential integral equation formulation of the problem, and the method of moments is employed to find the unknown surface current distributions on the strips carrying LR-SPP. In other words, in this method, the volumetric currents flowing inside the metal are substituted by a surface current model flowing on an infinitely thin strip characterized by the developed surface impedance model. This procedure reduces the number of unknowns significantly, in this way increasing the speed of simulation. Validity and accuracy of the proposed model are demonstrated by analyzing three popular LR-SPP circuits.