It is a question that has been asked many times, but little, apart from a certain amount of anguished hand-wringing, has been done about answering it.
The roots to it are many - deficiencies in the education system, parental preferences for steady careers in other professions such as law and accountancy and perception that engineering is dull and grimy work with few prospects, to name just a few.
Instead of just complaining, the profession is starting to do something about it. It is currently midway through a promotional exercise called Year of Engineering Success, which has the positive acronym Yes.
Its spokesman Michael Hird said the aim of the initiative, which is supported by the engineering institutes, industry and the Government, was to encourage young people - school leavers as well as graduates - to enter the profession. It is seeking to counter negative ideas about what it entails by promoting the idea that engineering is a profession in which the world is the individual's oyster. It was the only qualification which was standard around the globe, added Mr Hird.
Mr Hird acknowledges that even those graduates who find the idea of working as an engineer appealing are put off by the belief that it is badly paid. For instance, in recent years many engineering graduates and post-graduates have been lured into using their mathematical and related skills in high- earning jobs in the City. But the campaign is seeking to demonstrate that engineers are not necessarily paid less than professions requiring similar educational attainments, such as medicine and dentistry. Moreover, it claims that, for all the talk of British industry being run by accountants, 84 of the top 100 British companies have an engineer on their boards.
As the increasing prominence of high-technology companies demonstrates, a constant flow of engineering graduates into the work-force is essential if Britain is to compete on the world stage. According to Mary Harris, director-general of Yes, between 30,000 and 35,000 new engineers are needed every year, yet the number of people accepting places for engineering and technology degrees has fallen from more than 21,000 in 1992 to fewer than 18,000 last year.
The problem is being exacerbated by Britain's great success in attracting high levels of inward investment, which is causing problems in areas such as south Wales. Moreover, the even worse skills gap in the United States means that Seattle-based aircraft manufacturer Boeing and other companies are creating something like the "brain drain" that afflicted the UK of the 1960s by seeking to recruit engineers with the promise of large salaries.
Yes's programme amounts to a series of events - including exhibitions, talks in schools and open days designed to show that facilities operated by high-tech companies such as BT and Nortel are far removed from the conventional image of factories.
Some encouragement that all that weekend activity at the Science Museum might translate into the development of eager young engineers came earlier this spring, when more than 40,000 parents and young people - far more than the organisers expected - flocked to the Tomorrow's World Live exhibition in Birmingham to see demonstrations by the likes of Ford and BP and university research programmesn