NEW YORK — The U.S. natural gas market is bursting at the seams.

So much natural gas is being produced that soon there may be nowhere left to put the country’s swelling surplus. After years of explosive growth, natural gas producers are retrenching.

The underground salt caverns, depleted oil fields and aquifers that store natural gas are rapidly filling up after a balmy winter depressed demand for home heating.

The glut has benefited businesses and homeowners that use natural gas. But with natural gas prices at a 10-year low — and falling — companies that produce the fuel are becoming victims of their drilling successes. Their stock prices are falling in anticipation of declining profits and scaled-back growth plans.

Some of the nation’s biggest natural gas producers, including Chesapeake Energy, ConocoPhillips and Encana Corp., have announced plans to slow down.

“They’ve gotten way ahead of themselves, and winter got way ahead of them too,” said Jen Snyder, head of North American gas for the research firm Wood Mackenzie. “There hasn’t been enough demand to use up all the supply being pushed into the market.”

So far, efforts to limit production have barely made a dent. Unless the pace of production declines sharply or demand picks up significantly this summer, analysts say the nation’s storage facilities could reach their limits by fall.

That would cause the price of natural gas, which has been halved over the past year, to nosedive. Citigroup commodities analyst Anthony Yuen says the price of natural gas — now $2.08 per 1,000 cubic feet — could briefly fall below $1.