To distinguish between the various theories of plastic flow defining plastic stress-strain relations under combined stresses, it is necessary to conduct combined stress tests in which the ratio of the stress components does not remain constant during the test. To compare these results with the flow theory of the second stress-invariant type, graphical methods have been used to determine the combined plastic stress-strain relations based upon the simple tension plastic stress-strain relations. This paper presents an analytical procedure for the determination of these theoretical stress-strain relations. For certain stress conditions the graphical methods have the disadvantage of yielding inaccurate results—an objection not present in the proposed method. Furthermore, the proposed analytical method is less time-consuming than the graphical methods.