In current study, The Mesh-free method based on weak-form formulation coupled with the ultrasound imaging technique is developed. This problem consists in computing the deformation of an elastic non-homogenous phantom by numerical methods (both Mesh-free and Finite Element) and converge their results to the measured deformation by the ultrasound. The shape functions of Mesh-free are approximated by the Moving Least Square (MLS) method. The effect of Shape functions on the Mesh-free results are analyzed and discussed with the several simulations in 2D domain. پرونده مقاله