On the basis of a new WY-like representation block algorithms for orthogonal symplectic matrix factorizations are presented. Special emphasis is placed on symplectic QR and URV factorizations. The block variants mainly use level 3 (matrix-matrix) operations that permit data reuse in the higher levels of a memory hierarchy. Timing results show that our new algorithms outperform standard algorithms by a factor 3-4 for sufficiently large problems.