In this book, we will analyze the vibration of uniform and non-uniform beams resting on fluid layer in three cases; First: the free and forced vibration of uniform and non-uniform beams resting on fluid layer under axial force. Second: determination the static deflection behaviours of uniform and non-uniform beams resting on fluid layer under axial force and Third: the analysis of buckling behaviours of uniform and non-uniform bars resting on fluid layer under axial force which has been solved by the Differential Quadrature Method (DQM). We consider a homogeneous isotropic beam with various end conditions. In addition, the new algorithm implemented to solve engineering applications.