Sound transmission through flexible panels is investigated using Element Free Galerkin (EFG) method. In contrast to Finite Element Method (FEM), EFG method uses a set of nodes scattered within the problem domain and its boundaries to model the structure. These sets of nodes do not form a mesh, and hence information on the relationship between the nodes is not required for field variable interpolation.  Moving Least Square (MLS) approach is employed to generate the displacement functions in EFG method for vibration analysis of elastic structures. Subdivisions similar to finite elements are used to provide a background mesh for numerical integration. The essential boundary conditions are enforced by Lagrange multipliers for static problems. For analysis of free vibration and forced vibrations, the essential boundary conditions are imposed using orthogonal transform techniques. To demonstrate the validity and versatility of the method, modal analysis of beams and thin plates with different boundaries have been carried out. In addition, the response of these structures under dynamic excitation has been analyzed. The results obtained are in good agreement with those obtained by other methods. Sound transmission loss through panels with all edges clamped is investigated and the results are presented and discussed. Results are compared with those obtained from simple application of mass law and the agreement is quite good.