SHASTA LAKE, Calif.—One of the seemingly easiest ways to expand California’s water supply would be to raise the height of the 602-foot Shasta Dam by 18.5 feet, adding the equivalent of another reservoir to the drought-stricken state.

The federal Bureau of Reclamation has been studying the idea to some degree since 1980. But regulatory delays and pushback from critics—including a Native-American tribe that has performed war dances at the dam—prevented it from happening.

Raising the dam, which is a fairly common procedure though not on this magnitude, would cost about $1.3 billion. Getting the project funded through Congress and other sources, however, would be a challenge.

The hurdles in expanding the Shasta Dam underscore a broader problem in the nation’s most populous state as it grapples with a devastating four-year drought: state and federal officials haven’t significantly upgraded California’s water infrastructure in decades.

Building water projects amid divisions among residents in Northern California, where most of the water can be found, and Southern California, where most residents live, is a challenge. There are about 1,400 dams under state and federal control in California and roughly 1,300 reservoirs, officials said.