Effects of the taper angle and the angular velocity of a pulse tube on the enthalpy flow loss associated with the steady mass streaming were analysis by two-dimensional analysis of a pulse tube with variable cross-section. It was shown that the steady mass flux can lead to a large steady second-order temperature. The enthalpy flow loss associated with the steady mass streaming increases as the angular velocity increases. For a pulse tube where the viscous penetration depth is far thinner than the inner radius, the enthalpy flow loss can be significantly reduced by tapering the pulse tube since both the steady mass flux and the steady second-order temperature decrease as the taper angle increase.