The development of the H-bomb committed the United States to an arms race with the Soviet Union. Despite the specter of nuclear holocaust, both the United States and the Soviet Union vied to build ever more powerful nuclear weapons.
The Federal Civil Defense Administration was charged with creating shelter, evacuation, and training programs.
In the early 1950s, schools across the United States trained students to dive under their desks and cover their heads. Although these drills were designed to simulate what action should be taken during an atomic attack, they also heightened anxiety over an escalating arms race.

Nevertheless, duck and cover drills in use during the early 1950s, might have had some rationale. In the early ‘50s, Soviet atomic bombs were basically similar to bombs used in World War II—not the more advanced and large kind of atomic weapons they would later develop.
Main Source: History.com