We would like to show how inequalities at school in terms of success rate may entail significant social injustices concerning the access to a career in engineering. We have carried out research in two major engineering schools, in the Rhône-Alpes region in France, that each recruit more than a thousand students per year. These are the National Institute of Applied Sciences in Lyon (INSA) and the various schools composing the Grenoble National Polytechnic Institute (GINP). Through these data we can see how success at engineering school is linked to the parents' occupation. We have developed indicators to measure social representation in these schools so as to take into account the national occupational structure of the population. We have also studied some of the developments since the 1950s, when data are available. Today, the relative representation ratio between children of executives and higher intellectual professions and children of workers has increased to more than 20. We have especially referred to the theory of reproduction and to the theory of justice to highlight the social drawbacks which this entailed. We wanted to know where injustice lies: in the reproduction phenomenon or in the lack of equal opportunity. How to select excellent students with different and representative origins ? We have tried to find explanations for this phenomenon, engineering schools can focus on creating policy in order to reform such a trend, thanks to: tutoring in secondary education, special recruiting, individual support, awards, and incentive information toward the less advantaged students ...