The women, who have all suffered severe personal crises following undesired pregnancies, claim the law conflicts with their right to freedom from discrimination and protection against inhuman and degrading treatment.
"It is our assessment that the grounds under which these women are taking the case are very strong," said Ivana Bacik of the Irish Family Planning Association in a release Tuesday.
The association has been campaigning for free abortion since 1969. In 1983, a referendum decided that abortion should remain illegal. However, social circumstances have changed, with more than 6,000 women traveling to Britain for abortions last year, the IFPA said.
Ireland and Portugal are the only two countries in the European Union to deny women the option of abortion.