New additional conditions required for the uniqueness of the 2D elastostatic problems formulated in terms of potential functions for the derived Papkovich-Neuber representations, are studied.Two cases are considered, each of them formulated by the scalar potential function plus Ox bile one of the rectangular non-zero components of the vector potential function.For these formulations, in addition to the original (physical) boundary conditions, two new additional conditions are required.In addition, for the complete Papkovich-Neuber formulation, expressed by the scalar potential plus two components of the vector potential, the additional conditions established previously for the three-dimensional case in z-convex domain can be applied.To show the usefulness of these new conditions Goalie - Sticks - Junior in a numerical scheme two applications are numerically solved by the network method for the three cases of potential formulations.