For several types of continuum mechanics problems, the mesh is an issue in itself: it may be difficult to devise an appropriate mesh due to geometry complexity and/or the solution process may require frequent remeshing. The time taken in creating the mesh (or remeshing) is often several times more than the time needed to form and solve the system of equations. To avoid or reduce the mesh related difficulties, several alternative methods, commonly known as mesh less methods have been proposed: the Smoothed Particle Hydrodynamics Method (SPHM),the Reproducing Kernel Particle Method (RKPM), the Element-Free Galerkin Method (EFGM) and the Partition of Unity Finite Element Method (PUFEM), among others. One of mesh less methods is the Element-Free Galerkin Method (EFGM) which is used for vibration analysis of homogeneous rectangular thick plates based on First order Shear Deformation Theory (FSDT).