This paper discusses the use of two buoyancy schools in determining the axial forces in the drill string, which leads to the duality of the solution. The difference in the results in determining the true and effective force and their relationship with each other using the strength of stability were revealed. It is shown that only the true force can be used to calculate the stresses and deformations of the drill string elements, since their actual values correspond to this force. At the same time, taking into account the effective forces, it is possible to more fully use the actual stability of the drill string, increasing the permissible loads on the bit and increasing the penetration rate. Thus, the presence of two buoyancy schools and, accordingly, two types of axial forces, makes it possible to more accurately and comprehensively assess the operability of the drill string.