The Material Point Method (MPM) was originally formulated using structured background grids consisting of quadrilateral elements. Such grids and elements are advantageous since the location of material points in iso-parametric spaces becomes trivial. However, a major numerical issue arises with the use of such grids, which is critical in the case of implicit formulations of the MPM. In that case, rank deficiency can inevitably occur throughout a simulation causing numerical instability. Rank deficiency propagates throughout the domain, causing numerical dissipation and/or singularities. In the last two decades, solving the problem of rank deficiency in implicit MPM formulations has been a significant challenge. The use of “soft stiffness” became popular as a solution. Soft stiffness aims at improving the stability of an MPM model by adding a layer of material points to active cells, which helps prevent rank deficiency throughout the background grid. However, the problem of rank deficiency is overcome at the cost of more computations involving the calculation of additional stiffness at each of the extra material points that are added when using soft stiffness. A technique to overcome rank deficiency in the classical finite element theory is to use additional artificial stiffness only in the direction of hourglassing. In this study, soft stiffness and hourglass control are compared as stabilisation techniques against rank deficiency within an implicit MPM formulation. A benchmark of a simply supported beam is studied, and an application to a geotechnical stability problem of strength reduction is shown. This study proves that hourglass control is not only computationally more efficient but also more accurate than soft stiffness in plane conditions.