The BBC's CBeebies Storytime app has had more than four million story downloads since it launched a new library feature in June.
Top choices include The Clangers Space Tangle, voiced by Michael Palin, and Little Red Riding Hood, voiced by Maxine Peake.
Children can download up to 12 stories of their choice at a time and, like a real library, return them when they have finished.
Over the summer, the most popular time for families to download stories has been between 6pm and 7pm on weekdays and between 8am and 10am at weekends.
The CBeebies Storytime app, available to download free of charge in the UK via Apple iTunes, Google Play and the Amazon app store, aims to engage children in reading and storytelling.
The Clangers Space Tangle story launched on Thursday July 30 and became the most downloaded story of that week.
The top five most downloaded stories since the library feature launched are:
1. Justin's House - The Flying Duster
2. Ruff Ruff Tweet And Dave - A Fairytale Adventure
3. Something Special - Mr Tumble At The Park
4. The Clangers Space Tangle
5. Little Red Riding Hood
CBeebies controller Kay Benbow said: "We hoped our lovely library feature would be welcomed by parents as the app takes up less space on your device, but over four million downloads of stories in such a short space of time has truly exceeded our expectations."
The CBeebies Storytime app will welcome a host of new stories this autumn including The Furchester Hotel - The Very Helpful Guest and Show Me Show Me - Stuffy's Party.
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