A study carried out for the Sutton Trust recommended that this would be the fairest way to allocate places and give poorer pupils a better chance.
The research said that after factors such as home address, faith and siblings had been taken into account, names could be drawn at random to give everyone the same chance.
Sir Peter Lampl, chairman of the Sutton Trust, wrote in the foreword: "Deployed alongside other selection criteria, ballots are the fairest way of deciding school places in over-subscribed schools. There has to be some way of choosing which pupils are admitted, and ballots offer the same chances to all children irrespective of their background."
The report was written by Alan Smithers and Pamela Robinson from the Centre for Education and Employment Research at the University of Buckingham.
Former studies by the trust which look at school admissions have been based on the number of children receiving free school meals, but this focused on the number whose families were on benefits. The researchers looked at data called the Income Deprivation Affecting Children Index.
The Sutton Trust works to boost social mobility through education.