Because this question was originally under the "Health" category, it will be assumed that the questioner is focusing on disaster preparedness for hospitals.
Especially since the terrorist attacks of September 11, 2001, there is a tremendous amount of attention and resources devoted to disaster preparedness. Certain regions of the country where natural disasters are recurring events, mainly the hurricane zone from the Carolinas down through the Gulf Coast, have long been attuned to the need for disaster preparedness policies. The terrorist attacks and the spread of natural disasters to geographical regions where they were not previously endemic has forced the entire country to think more about that problem.
While the focus of this answer will be on hospitals, it should be emphasized that proper training and equipping of so-called "first-responders" like police and fire departments has become a high priority in many American cities and towns. As the first on the scene of a disaster, the police and fire departments play a vital role in responding to the mass-casualty scenarios associated with natural and man-made disasters. They have to be trained and equipped to immediately identify the source of the problem, for example, the release of a chemical agent or the radiation associated with a so-called dirty bomb, and to begin providing relief while securing the perimeter around the disaster.
With respect to hospitals, certain procedures are required to be prepared for a catastrophic event. First, staff must be trained to handle both the drastically-increased patient load that would inevitably follow a disaster and the emotional fallout that would also deluge medical facilities as families of the injured pour in seeking help and answers.
Second, adequate inventories of vital equipment and supplies must be maintainted, with constant attention to ensure that all such supplies, for example, plasma, antibiotics, iodine (used both for cleaning and for treating effects of radiation), are within their expiration dates. Discovering that inventories of medications are expired after the disaster occurs is too late for immediate treatment of patients. In addition, because the catastrophic event can shut down energy supplies, the facility must be equipped with sufficient back-up generators to ensure vital services can continue.
Third, as with the hospital staff, the security staff must be trained to handle the increased flow of patients, families, and individuals simply seeking shelter. Failure to have a large-enough and highly trained security staff will result in problems when hundreds or thousands of panicked people flood the facility. Crowd control within the confines of a facility like a hospital is difficult, but it is essential.
Fourth, communications links with the outside world must be ensured through redundancy. The ability to communicate with police and fire departments and with other medical facilities is extremely important.
Because catastrophes can take many forms, especially with the increased risk of terrorist attacks over the past decade, it is difficult to prepare for every contingency. The threat of a terrorist attack utilizing chemical weapons like sarin or biological weapons like anthrax, plague, and many others requires a wide-range of contingency planning, as antidotes and treatments differ for each substance. places a heavy burden on hospitals and governments trying to be prepared for all scenarios.