The High Court has been told that under the Constitution, the Federal Government did not have the power to set up the National School Chaplaincy Program.

The chaplaincy program was set up in 2007 to provide for the spiritual wellbeing of students, and school communities are able to determine the criteria on which chaplains should be employed.

But lawyers have told the High Court the program is invalid because the Constitution bans a religious test from being a qualification for those paid by the Commonwealth.

Lawyer Brett Walker also told the court the benefit to students from the program cannot be compared to things like a national literacy or numeracy program.

He is arguing the Government may have gone far beyond its power in appropriating the money for such a program.

The man behind the High Court challenge, Queensland father Ronald Williams, says he is encouraged by support for his case from the states.

The states will argue the Federal Government overstepped its authority by funding the program.

The Greens also hope the school chaplaincy program will be scrapped.

Greens Senator Sarah Hanson-Young says school support staff should have qualifications rather than religious affiliations.

"The money that is currently there should be put towards a student support program where we have youth workers or counsellors or people to liaise between students and government agencies for example, whatever the needs of those students are, but first and foremost, those people have to be qualified," she said.

But the Government and Scripture Union Queensland are fighting the case to maintain the program.

Tim Mander from Scripture Union says school chaplains are no different to those in the military or police.

The case continues.