Judge James O’Donoghue dismissed the cases of Eileen Ward and Charlie Ward when they appeared at Letterkenny Circuit Court in Co Donegal.
The pair, who are related by marriage, were both claiming against the driver of the car, Mr Ward’s wife Kathleen, following a collision at Ratoath in Co Meath in February 2012.
Both gave evidence that they suffered neck and back injuries as a result of the accident and were suing Liberty Insurance for personal injuries.
The amount of financial damages being sought by both people was not disclosed during the case.
However, the court was told there was minimal impact in the crash.
Two other people in the car had also started personal injury claims against the driver but one had already been struck out.
The incident happened when the Nissan Primera being driven by Kathleen Ward, slid into the back of a car stopped at a set of traffic lights at Fairyhouse, Ratoath.
There were five occupants in the car including Eileen Ward, Charlie Ward, Kathleen Ward, another Charlie Ward and a cousin Michael Mongan.
The Toyota Corolla car parked at the red traffic light was being driven by computer science student Liviu Ioan Pantille, who was returning from lectures at Maynooth University.
Mr Pantille was unhurt in the incident and paid the €100 to repair the tow bar of his car out of his own pocket, the court heard.
In a report, Dr Martin Coyne compared the injuries suffered to that people might receive in a bumper car incident at a fairground.