DETROIT — The U.S. auto industry, already stretching to meet rising demand for cars and trucks, is facing shortages of parts and materials that could limit the number of new vehicles in showrooms later this year and crimp a historic turnaround.

The most immediate problem — a shortage of a crucial plastic resin, caused by an explosion March 31 at a plant in Germany — could surface in a few weeks. And later this year or beyond, automakers could be confronted with an even bigger crisis, running short of parts simply because there aren’t enough factories and people to make them.

No one is entirely sure how many plants or models will be affected by either problem. Automakers say they are working to avoid shortages in both cases. But it may be tough to manage the intricate chain of companies that make most of the 3,000 parts that go into every car, from tiny valves and computer chips to heavy metal castings for transmissions.

“A lot of them are under pressure because they reduced their staff and temporarily mothballed some of their factories,” said Jim Gillette, an analyst with IHS Automotive. “A number of them are struggling to keep up at the moment.”

The broader parts shortage dates to the auto industry’s near-collapse in 2008 and 2009, when sales plummeted and General Motors and Chrysler were forced into bankruptcy protection.

During the downturn, at least 57 parts makers closed, were bought out or went into bankruptcy, according to the Original Equipment Suppliers Association. Nearly 20 percent of auto parts workers — more than 100,000 people — lost their jobs from 2008 through 2011.

U.S. auto sales dropped to a 30-year low of 10.4 million in 2009 but are on the rebound. Last year, they grew to 12.8 million, and analysts are predicting 14.5 million or more this year. If sales rise above 15 million, experts say some automakers will run short of parts, crimping the supply of certain models.