In this paper we propose a parallel implementation of the FSAI preconditioner to accelerate the PCG method in the solution of symmetric positive definite linear systems of very large size. This preconditioner is used as building block for the construction of an indefinite Inexact Constraint Preconditioner (ICP) for saddle point-type linear systems arising from Finite Element (FE) discretization of 3D coupled consolidation problems. The FSAI-ICP preconditioner, based on an efficient approximation of the inverse of the (1,1) block proves very effective in the acceleration of the BiCGSTAB iterative solver in parallel environments. Numerical results on a number of realistic test cases of size up to 6 million unknowns and 300 million nonzeros show the almost perfect scalability of the overall code up to 512 processors
