The institute commissioned the study of teachers, educationists and more than 700 pupils to inform its new website for engineering teachers and pupils.
It found that two-thirds of pupils believed engineering was important to society, but some, girls especially, still saw it as a dirty, manual job.
"An engineer wears overalls, dirty clothes and a hard hat," said one.
Pupils rated it 11th on a list of preferred careers, far behind favoured occupations like law, teaching and professional sport.
Teachers and engineering instructors consulted for the report said pupils needed to be told how much money they could earn in engineering and that it was a chance to make their mark on the world.
"Pay engineers lots of money and then let people know about it," one engineer said.