Applicants will argue climate change threatens their rights including to life, physical and mental wellbeing.
Current policies would fail to meet either goal, according to the United Nations' Intergovernmental Panel on Climate Change.
"Without urgent action to cut emissions, (the place) where I live will soon become an unbearable furnace," another applicant, 20-year-old Martim Agostinho, said in a statement.
Last month, a judge in Montana, in the United States, handed a historic win to young plaintiffs in a climate change case.
In addition to Wednesday's youth case, there are two other climate cases pending before the ECHR's Grand Chamber.
Persons:
Catarina Demony, Gerry Liston, Andre Oliveira, Martim Agostinho, Agostinho, Liston, Aislinn Laing, Alex Richardson
Organizations:
European, of Human Rights, United Nations
Locations:
Portugal, Britain, Switzerland, Norway, Russia, Turkey, Strasbourg, Paris, Portuguese, Leiria, Europe, Montana, United States, Lisbon