Abstract: Finite element method is one of the most efficient numerical methods for the solution of three-dimensional elasticity problems. In practice, the mesh geometry and mesh quality may have a great effect on the algebraic solvers. In this work, we have presented some numerical studies for evaluating the effectiveness of several commonly used algebraic multigrid (AMG) methods on some typical meshes. We can obtain much more robust and efficient AMG iteration by using the known information that is readily available in most finite element applications, for instance, the type of the partial differential equations (PDEs) considered and the number of physical unknowns residing in each grid, and by combining the coarsening techniques used in the classic AMG method. The efficiency and robustness of the resulting AMG methods are also confirmed by some numerical tests.