The campaign is part of a competition that has been inspired by an increasing number of people travelling with the airline who have been leaving poems on the bags for the next passenger to find.
The entries will be judges by Daisy Goodwin, the writer and TV producer behind ITV drama Victoria.
To enter the competition people will need to write their poem on a sick bag and then share an image of it on Twitter or Instagram with @easyJet using the tag #LoveSickSonnets. The winner will be awarded a pair of easyJet flights.
Tina Milton, head of cabin crew at easyJet, said: "Distance is said to make the heart grow fonder, but long-distance relationships are always hit with some light turbulence.
"We are challenging our customers to channel their inner Byron, Keats and Wordsworth and pen some romantic lines on the back of our passenger sick bags."
The campaign has been created by Taylor Herring with VCCP working on the social.
The video below shows footage from EasyJet's pop-up café in London last year, which was launched to target 'Generation EasyJet' and promote spontaneous travel.