Abstract: To enforce accurate displacement constraints,essential boundary conditions and interface continuity conditions in mesh-less method are treated as Multi-Point Constraints (MPC) of displacement,which are illustrated by using SPH (Smoothed Particle Hydrodynamics) method incorporated with algebraic master-slave relations.An example of linear elastic problem of representative volume element in matrix-inclusion composite is presented.Numerical tests show that the proposed algebraic master-slave method leads to higher accuracy and wider application than the penalty function method.