Since parallel computers have different performance ratios of computation and communication, the optimal computational block sizes are different from one another to generate the maximum performance of an algorithm. Too small or large a block size makes getting good performance on a machine nearly impossible. In such a case, getting a better performance may require a complete redistribution of the data matrix. We present PoLAPACK factorization routines, including LU, QR, and Cholesky factorizations, with an "algorithmic blocking" on 2-dimensional block cyclic data distribution. With the algorithmic blocking, it is possible to obtain the near optimal performance irrespective of the physical block size. The routines are implemented on the SGI/Cray T3E and compared with the corresponding ScaLAPACK factorization routines.