An American Airlines flight carrying 154 people skidded across a Jamaican runway in heavy rain, bouncing across the tarmac and injuring more than 40 people before it stopped just short of the Caribbean Sea, officials and witnesses said.

Panicked passengers screamed and baggage burst from overhead bins as Flight 331 from Miami careened down the runway in the capital, Kingston, on Tuesday night, one passenger said.

The impact cracked open the fuselage, crushed the left landing gear and separated both engines from the Boeing 737-800 ...