Numerical results for the steady natural-convection heat transfer in a tilted cylindrical envelope with constant but different end temperatures (300 versus 80 K) and an adiabatic lateral wall are presented. This envelope is supposed to be a simplified model for the pulse tube in a pulse-tube cryocooler when the pulse tube is positioned at different orientations. Variation of the average heat transfer rate with the inclination angle, and details of velocity and temperature distributions, are provided for four typical inclination angles. The major numerical results are as follows. First, the flow pattern caused by the natural convection in the pulse tube is very complicated, characterized by the global circulation between the hot and cold end accompanied by several local recirculations, leading to a multicell structure of flow pattern. Second, from the temperature distribution, especially the section average temperature distribution, the heat transport mechanism of natural convection in the pulse tube may be classified into two classes, conduction-dominated and convection-dominated. The maximum heat transfer rate occurs at inclination angle of 120 . Comparisons with available test results are made, and the agreement between the predicted and the test data is reasonably good. Third, even for the conduction-dominated case, there exists very weak flow within the pulse tube. Finally, to reduce the loss of cooling capacity a pulse tube in operation should be positioned in the range of inclination angle from 0