A new IC interconnect transmission line parameter determination methodology and a novel fast simulation technique for non-uniform transmission lines are presented and verified. The capacitance parameter is a strong function of a shielding effect between the layers, while silicon substrate has a substantial effect on inductance parameter. Thus, they are taken into account to determine the parameters. Then the virtual straight-line-based per unit length parameters are determined in order to perform the fast transient simulation of the non-uniform transmission lines. It was shown that not only the inductance effect due to a silicon substrate but also the shielding effect between the layers are too significant to be neglected. Further, a model order reduction technique is integrated into Berkeley SPICE in order to demonstrate that the virtual straight-line-based per-unit-length parameters can be efficiently employed for the fast transient response simulation of the complicated multi-layer interconnect structures. Since the methodology is very efficient as well as accurate, it can be usefully employed for IC CAD tools of high-performance VLSI circuit design.