British champion Jack Laugher missed out on a place in the individual 3m springboard semi-final but team-mate Chris Mears progressed.
Laugher, 17, was the youngest diver in the competition and after reaching the world championship final last year, was expected to make the next round.
The teenager finished 27th, while Mears grabbed the last qualifying position in 18th with 436.05 points.
Russia's world silver medallist Ilya Zakharov leads the standings.
China's defending champion He Chong recorded the second-highest score in the preliminaries with 500.90, behind Zakharov's 507.65.
Two-time world and European junior champion Laugher struggled throughout the competition and failed to complete his final routine after mistiming his approach.
German Stephan Feck's bid to progress also ended after a disastrous dive in the second round, when he landed on his back as he entered the water.
Double Olympic silver medallist Alexandre Despatie, who needed 21 stitches after hitting his head on the board just six weeks ago, came through in ninth.
He and Mears, who partnered Nick Robinson-Baker to a fifth-place finish in the synchronised event, will now return to the Aquatics Centre for the semi-finals on Tuesday morning.
Divers will then be searching for a top-12 position in order to reach the final at 19:00 BST on Tuesday evening.