Parallel conductance (electric current flow through surrounding tissue) is an important determinant of accurate measurements of arterial lumen diameter, using the conductance method. The present study is focused on the role of non-uniform geometrical/electrical configurations of surrounding tissue, which are a primary source of electric current leakage. Computational models were constructed to simulate the conductance catheter measurement with two different excitation electrodes spacings (i.e. 12 and 20 mm for coronary and peripheral sizing, respectively) for different vessel-tissue configurations: (i) blood vessel fully embedded in muscle tissue, (ii) blood vessel superficially embedded in muscle tissue, and (iii) blood vessel superficially embedded in muscle tissue with fat covering half of the arterial vessel (anterior portion). The simulations suggest that the parallel conductance and accuracy of measurement is dependent on the inhomogeneous/anisotropic configuration of surrounding tissue, including the asymmetric dimension and anisotropy in electrical conductivity of surrounding tissue. Specifically, the measurement was shown to be accurate as long as the vessel was superficial, regardless of the considerable total surrounding tissue dimension for coronary or peripheral arteries. Moreover, it was shown that the unfavourable impact of parallel conductance on the accuracy of conductance catheter measurement is decreased by the combination of a lower transverse electrical conductivity of surrounding muscle tissue, a smaller electrode spacing and a larger lumen diameter. The present findings confirm that the conductance catheter technique provides an accurate platform for sizing of clinically relevant (i.e. superficial and diseased) arteries.