There is no question that geometric and elastic tapering is the rule of the nature of the mammalian arterial system. In this investigation, we determine the role of an exponentially tapered T-tube model to characterize the non-uniform nature and physical properties of the vasculature. The tapering feature could be inferred to show a connection between characteristic impedance at the distal of the tube and that at the entrance of the tube. Pulsatile pressure and flow signals of the ascending aorta were measured in 12 closed-chest, anesthetized dogs. This non-uniform T-tube model fits the measured aortic pressure waveform well. The mathematical and experimental model impedance spectra are similar. In the basal state, the distal characteristic impedance is 9.5% higher than the input characteristic impedance. The input characteristic impedance estimated in the model is compatible with that calculated by averaging high-frequency moduli of impedance data points obtained from the ratio of the corresponding harmonics of pressure and flow. Furthermore, the exponentially tapered T-tube model has a close estimate in wave transit time when compared with that computed by the impulse response of the filtered aortic input impedance. These data suggest that inclusion of tube tapering improves the mathematical model so that it is capable of characterizing the non-uniform nature of the arterial system. We conclude that the non-uniform properties of wave-transmission paths play an important role in governing the behavior of an asymmetric T-tube for the representation of the arterial system.