Schools in England could need an extra 19,000 head teachers and deputies within the next six years, education charities are warning.
The Future Leaders Trust, Teach First and Teaching Leaders say the new leaders will be needed as pupil numbers rise and large numbers of heads retire.
They also highlight the need for extra school leaders as more schools switch to academy status.
The Department for Education says it does not recognise the figures.
The latest school workforce data shows that there are 68,800 full-time equivalent leaders in state schools in England.
The DfE adds that since 2010 the proportion of schools reporting a head teacher vacancy has decreased, while the number of school leaders over the age of 50 has decreased significantly.
But a report by the charities, entitled the School Leadership Challenge, says that 3,800 schools do not have enough leaders currently to enable them to operate in the best way possible.
And it calculates that while between 16,000 and 20,000 heads and deputies will reach retirement age by 2022, there are not enough teachers coming through schools to replace them.
About 65% of school leaders are aged over 45, which means there will be large numbers of retirements over the next 10 to 15 years, the report says.
It also argues that as more schools convert to academy status there will be a need for between 4,000 and 8,000 more leaders, as the academy programme tends to create another level of management.
Most trusts tend to have a chief executive officer and an executive head overseeing a number of schools, and these posts are pulling large numbers of senior head teachers out of traditional school headship roles.
'Action needed now'
And through a complex model including population projections, retirement rates and predicted rates of conversion, the report concludes some 19,000 head teachers will be required.
It says schools already face recruitment challenges, with many struggling to attract high quality applicants and spending thousands of pounds on recruitment campaigns.
Salaries for head teachers vary from around £54,000 at a primary school to as much as £108,000 at a large secondary.
Chief executives running a number of schools in an academy chain can earn £250,000 a year.
The charities recommend one way to ease the shortage would be to recruit executives from other organisations or business to run schools.
Malcolm Trobe, interim general secretary of the Association of School and College Leaders, said: 'Many more school leaders will be needed over the next few years and it is vital to take action now to address this issue.'