*Result*: The method of fundamental solutions for solving direct and inverse Signorini problems in elasticity.

*The method of fundamental solutions (MFS) is a meshless boundary collocation method the implementation of which is very simple rendering the numerical solution of challenging boundary value problems such as free boundary and inverse problems. For this reason, in the current study we apply the MFS for the solution of a specific category of two–dimensional free boundary value problems in elasticity, namely, Signorini problems. We demonstrate that the proposed method is ideally suited for solving such problems. In the MFS, the displacement and traction are approximated by linear combinations of fundamental solutions with sources located outside the closure of the solution domain. The unknown coefficients in these expansions as well as the separation points on the Signorini boundary are determined by imposing/collocating the boundary conditions which can be of Dirichlet, Neumann or Signorini type. The MFS reformulation results in a constrained minimization problem which is solved using the MATLAB® optimization toolbox routine fmincon. The proposed technique is applied to problems from the literature previously solved using the boundary element method. [ABSTRACT FROM AUTHOR]*