The yield locus (YL) of powder bed can be used to determine many mechanical properties of a powder such as cohesion, unconfined yield stress, stress ratio, etc. Generally, the YL of powder beds is obtained by fitting the results of shear tests to linear approximations based on the Coulomb equation or to curved approximations based on the Warren-Spring equation. Meanwhile, the yielding characteristics of a powder bed are expressed by the Roscoe condition diagram. In this diagram, the YL appears orthogonal to the normal stress axis at both ends corresponding to tensile and compressive strength. However, the YL approximated by the Coulomb or Warren-Spring equations is not orthogonal to the normal stress axis at both ends, and is not the same shape as the YL shown in Roscoe condition diagrams. Thus, the abovementioned mechanical properties obtained from the YL of a powder bed are likely to be affected by the approximate expression for the YL. Despite this, no one has investigated how the mechanical properties of powder beds such as stress ratios are affected by the approximation method for the YL. In this paper, we propose a new approximation equation for the YL that conforms both to the shape of the YL in the Roscoe condition diagrams and experimental results. Then, these YL obtained by our equation, and by the Coulomb and Warren-Spring equations are used to determine the mechanical and flow properties of powder beds. These values are compared with each other in order to discuss the validity of our equation.