In this paper,aboundary-type meshless numerical scheme,based on the singular boundary method(SBM),is proposed to efficiently analyze the two-dimensional Signorini problems.The mathematical formulation of the Signorini problem can be used to describe various engineering problems,such as the shallow dam problem,the free boundary problem,unilateral contact problem,etc.In Signorini problem,either Dirichlet boundary condition or Neumann boundary condition with inequality constraints are imposed on some boundary segments.In addition,the number and the positions of the boundary points,where the boundary conditions change,are unknown.Thus,it is necessary to develop an efficient and accurate numerical scheme for numerical solutions of the Signorini problems.In order to deal with the Signorini problems,we adopted the Fischer-Burmeister NCP-function to convert the troublesome boundary conditions to nonlinear boundary conditions.The SBM,a newly-developed boundary-type meshless method,is used to analyze the two-dimensional Laplace problem with nonlinear boundary conditions.The numerical solutions of SBM are expressed as linear combinations of fundamental solutions with different strengths.Unlike the method of fundamental solutions,the sources of the SBM are exactly placed along the physical boundary.The source intensity factors,which appear when source and boundary collocation node coincide,are derived by using a subtractingand adding-back technique and the inverse interpolation technique.Since the fundamental solutions already satisfy the governing equation,the unknown coefficients of the solution expressions can be acquired by enforcing the satisfactions of boundary conditions.Because the derived boundary conditions in the Signorini problems are nonlinear,to use the SBM will also result in a system of nonlinear algebraic equations,which are then efficiently solved by the Newton-Raphson method.Several numerical examples are provided to verify the merits of the proposed meshless numerical scheme.In addition,some factors of the proposed numerical scheme are numerically examined via a series of numerical experiments.