Abstract: A type of algebraic multigrid (AMG) method and the corresponding preconditioned conjugate gradient (AMG-CG) algorithm, which are applicable to three-dimensional elasticity problems discretized with equal algebraic structure partitions on each layer, are developed. The technique of selecting coarse grids and the method for constructing the corresponding interpolation operator or restriction operator are discussed in detail. Application to some practical linear elasticity problems such as the problems with jumps in Young's modulus and high stress gradients is further studied using the AMG method and the AMG-CG method. Numerical results show that the AMG method and the AMG-CG method are very efficient and robust in comparison with direct methods and other iterative methods.