The influence of the loading program on the agreement between the predictions of the Hencky and the Prandtl-Reuss stress-strain relations for a perfectly plastic material is investigated in the case of the combined bending and twisting of thin-walled tubes. The agreement in the values of the bending and twisting moments is found to vary considerably with the particular loading program chosen. The analysis is extended to tubes composed of a work-hardening material. The bending and twisting moments are obtained numerically using the incremental approach for a square tube which is bent and then twisted. Owing to the large amount of labor involved in this solution, an approximate method using the concept of a “composite” beam is developed, and good agreement in the results is found with those obtained from the incremental solution.