A two-dimensional model for pulse tubes with tapered cross-section was proposed. Net enthalpy flow and steady mass streaming were investigated by two-dimensional analysis of mass, momentum and energy equations of the gas as well as energy conservation of the tube wall. Steady mass flux profiles show good agreement with the previous approximate solution. It was shown that steady mass streaming can be reduced by tapering a pulse tube and by increasing the length of a pulse tube. Effects of the velocity phase angle and frequency on steady mass streaming were shown