Abstract The application of a parallel multiblock geometric multigrid is consid-ered. It is applied to solve a two-dimensional poroelastic model. This system of PDEs is approximated by a special stabilized monotone finite-difference scheme. The obtained system of linear algebraic equations is solved by a multigrid method, when a domain is partitioned into structured blocks. A new strategy for the solution of the discrete problem on the coarsest grid is proposed and the efficiency of the obtained algorithm is investigated. The geometrical structure of the sequential multigrid method is used to develop a parallel version of the multigrid algorithm. The convergence properties of several smoothers are investigated and some computational results are presented.