Undrained shear strength (su) is one of the key geotechnical parameters for both natural and remolded soils. While it is basically a function of water content, it is also related to soil plasticity. There has been a long-lasting debate as to whether the su at the plastic and liquid limits are constant and whether the ratio of the su at the plastic limit to the su at the liquid limit is mostly fixed to 100. While this view is embraced by a great majority of researchers, some proclaim that the range of both the su at the plastic limit (PL) and the su at the liquid limit (LL) is rather wide; therefore, constant values of the su cannot be assigned for either the PL or the LL. Accordingly, the view that there is a constant ratio between the two shear strengths is invalid. The scope of this investigation is to reassess this problem using the laboratory vane shear test (VST) along with a new supplementary tool, the mud-press machine (MPM). Sixty remolded soil samples were employed as the study material. The variation of soil strength at both the plastic and liquid limit is investigated using the VST and MPM methods. While the VST method does not portray a distinctive relationship between the su and the two Atterberg limits, the newly introduced MPM method clearly shows that there is a meaningful relationship between the extrusion force, which is considered akin to the undrained shear strength, at the Atterberg limits and the two consistency limits, particularly the liquid limit. Concerning the constant ratio between the two shear strengths, namely the one at the plastic limit to the one at the liquid limit, it was found that this ratio is a constant, but it increases with the increase in soil plasticity.Keywords: Undrained shear strength, soil plasticity, vane shear test, mud press method, remolded soils.