Multilayer (ML) plate/shell finite elements (FEs) based on a versatile higher-order-deformable (HOD) theory are developed for free vibration analysis and damping prediction of damped composite laminates. The developed FEs allow one to arrange through-the-thickness degrees of freedom (DOF) by specifying the degrees of multilayer dicretization (ML, or Equivalent-Single-Layer : ESL) and deformation assumptions (First-Order-Shear-Deforable : FOSD, or HOD). By comparing the numerical results of the present FEs wih each other and the available experimental results, numerical accuracies of four different types of rough-the-thickness DOF arrangement, that is, ESL/FOSD, ESL/HOD, ML/FOSD and ML/HOD, are investigated for free vibrations of CFRP laminates with constrained viscoelastic damping layers.