Reading Borough Council says every family who applied for a primary school place in the town starting in September will be offered a place - but less than 80% will receive their first choice.
It says its continuing to suffer an increase in the population of primary school aged children.
A total 2,138 applications were received for the September 2013 intake, just six short of the total number of applications received last year, which in itself was an increase of nearly 200 applications from 2011 the figure.
Initial data for primary school applications in Reading shows:
First choice preferences have increased by just 1.3% to 77.4% as a result of extra classes being added to schools
The number of pupils receiving one of their top three preferences increased by 3.2% to 93.5%
However, the number of families offered a place at a school they did not list on their application still stands at 4.4%
The recent Census shows a 34% increase in children aged 0-4 years old - the second highest rise in the whole of the South-East since 2001.