Police were alerted to the accident at junction 27 of the eastbound M62 at Birstall just before 8am.
Two lanes of the eastbound M62, which were closed after the accident, have now been re-opened.
However, long delays are still being reported on the eastbound M62 and Highways England are advising drivers to consider alternative routes.
The accident involved a white Iveco HGV, a silver Vauxhall Corsa, a grey Skoda Superb and a silver Hyundai Sante Fe.
Two drivers were taken to Leeds General Infirmary for treatment to minor injuries.
Traffic queues were also being reported this morning due to fog on the M1 northbound between junction 37 and junction 42.