We present in this paper multi-thread and multi-process parallelizations of the Fast Multipole Method (FMM) for Laplace equation, for uniform and non uniform distributions. These parallelizations apply to the original FMM formulation and to our new matrix formulation with BLAS (Basic Linear Algebra Subprograms) routines. Differences between the multi-thread and the multi-process versions are detailed, and a hybrid MPI-thread approach enables to gain parallel efficiency and memory scalability over the pure MPI one on clusters of SMP nodes. On 128 processors, we obtain 85% (respectively 75%) parallel efficiency for uniform (respectively non uniform) distributions with up to 100 million particles.