Describing it as 'soft porn' and offensive to families, the image features Israeli supermodel Bar Refaeli, currently dating actor Leonardo DiCaprio, lying down in a brief white bikini. It is part of a promotional deal with Sports Illustrated magazine.

The plane was unveiled this month reported news website news.com.au and services all of Southwest routes.

Passengers have inudated the corporate blog about the image, complaining a bout having to fly in a plane 'covered in pornography', said the report.

'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.'

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

However some customers have defended the airline saying that Southwest is known for its 'fun attitude'.

The plane will be repainted in regular livery when the promotion ends in a few months.