An anchor system for temporarily anchoring the lower end of a lower marine riser package (LMRP) assembly, drilling riser, and drill string used in drilling subsea wells. The anchor system includes a dummy wellhead secured to the ocean floor and weight means stored in a dummy wellhead that can be connected to the end of the drill string in a manner that restrains the lateral movement of the LMRP assembly, drilling riser, and drill string.