In this paper, a new mesh domain partition strategy called the multi-type partition is introduced and applied to define new block parallel SOR (BPSOR) methods for solving 2D or 3D elliptic boundary problems. Based on strip and block mesh partitionings, three particular multi-type partitions are proposed, which lead to three BPSOR methods. A general mathematical analysis shows that the BPSOR method can have the same asymptotic convergence rate as the corresponding sequential block SOR method. Numerical results confirm such a theoretical claim and show that the BPSOR method has good parallel performances on a parallel MIMD computer.