After some remarks on the parallel implementation of the Finite Element package FEAP, our realisation of the parallel CG-algorithm is sketched. From a technical point of view, a hierarchical preconditioner with and without additional global crosspoint preconditioning is presented. The numerical properties of this preconditioners are discussed and compared to a Schur-complement-preconditioning, using a wide range of data from computations on technical and academic examples from elasticity.