Israeli supermodel Bar Refaeli, currently dating actor Leonardo DiCaprio, is pictured lying seductively in a revealing white bikini along the length of the Boeing 737 as part of a promotional deal with Sports Illustrated.

The latest addition to the US-based airline was unveiled this month and is deployed like other aircraft in the fleet, servicing all its routes.

The airline has received a flood of criticism on its corporate blog about the promotion, with many passengers complaining about having to board an aircraft “covered in pornography”.

Sexy: See the bikini-clad model on the plane

“I would not want to have to watch this plane pull up to the gate traveling with my young child, or mother, grandmother, etc,” customer Jim Dawson said.

“I know Southwest is known for its fun, laid back qualities but this is just completely inappropriate to plaster all over the side of the plane.”

Mr Dawson was not alone in his disapproval, with many passengers slamming the aircraft as being in poor taste.

“(It’s) very tacky. I know Southwest is notorious for it's fun, but this is simply in bad taste,” Don said.

“This looks like a flying porn ad! I'm a longtime fan of SWA, this is one reason for me to change airlines,” another customer, Yvonne, said.

Refaeli isn't the first attractive woman to be featured in a Southwest promotion. The airline aired television commercials in the 1970s starring flight attendants clad in hot pants and go-go boots, a uniform said to be favoured by co-founder Herb Kelleher.

The low-cost airline hit the headlines in 2007 when a Southwest Airlines employee allegedly ordered a passenger off a flight for wearing a revealing outfit.

Kyla Ebbert, 23, from San Diego claims she was only wearing a snug-fitting white top with a scoop neck that stopped just short of showing cleavage during the incident.

Southwest later apologised to Ebbert and launched a fare sale that included "miniskirt prices".

The bikini jet has some customers calling for a boycott of the airline, with others defending the promotion.

The paint job will be removed when the promotion ends within a few months.