A group of principals has called on schools to stop academic selection.
A hard-hitting statement describes the testing of 10 and 11-year-olds as an "annual charade".
Grammar schools have now used their own exams in place of the eleven plus to select pupils two years running.
The Catholic Principals Association, which claims to represent the majority of Catholic primary and secondary schools, says grammar schools should not "pick and choose" their pupils.
Instead it urges them to embrace a fully inclusive system.
It has a particular message for Catholic grammar schools, which show little sign of moving towards the end of academic selection, against the wishes of the bishops.
It says the use of unregulated tests by those schools flies in the face of advice from the commission for Catholic education.
The statement is timed to coincide with letters to parents telling them which schools have accepted their children for the next academic year.