Longitudinal vibration of a bar of general taper is analyzed subject to the inclusion of the effect of Poisson's ratio. The resulting differential equation may be used to treat bars of general taper. Numerical results are presented for bars of conical taper. It is found that if the length of the bar exceeds the diameter then inclusion of a value of Poisson's ratio equal to 0.3 leads to the prediction of fundamental resonant frequencies and velocity gains that are only a few percent less than the predicted values that result when Poisson's ratio is ignored.