RENTON, WA—Boeing Co. is facing a problem as it races to meet demand for single-aisle, fuel-efficient jets: Where to store unfinished 737s piling up at its factory near Seattle. Ine answer in late July was the taxiway of the small airport here, next to Boeing's factory there, reports the Wall Street Journal.

“Boeing is running out of space,” Renton public works administrator Gregg Zimmerman wrote to city council members in a July 27 memo about the taxiway plan. “They have encountered an emergency production challenge that threatens to interfere with their ability to keep their airplane production lines running.”

A Boeing spokesman said the request for parking space was part of a “recovery plan” to get deliveries to match production rates. Zimmerman declined to comment.

The unfinished airplanes illustrate a challenge to Boeing, the world’s biggest aircraft manufacturer by sales, as it tries to make enough of its new 737 Max jets to meet fast-growing demand. Boeing and rival Airbus SE together have more than $1 trillion in orders for planes, driven by a global boom in air travel that is adding 100 million passengers a year.

Boeing delivered just 29 of the 737s in July, though more than 50 mostly-finished jets roll off the production line each month. Company officials have said deliveries could slow in the third quarter but pick up in the fourth as suppliers get back on track. The 737 is Boeing’s most popular commercial aircraft and a top moneymaker that has helped propel the company’s stock more than 40% in the past 12 months.

The delays are due largely to two suppliers: engine maker CFM International, a joint venture between General Electric Co. and Safran SA, and fuselage manufacturer Spirit AeroSystems Holdings Inc. Both companies have said some of their own small suppliers are struggling to meet demand.