The two sisters and their brother, whose parents originally came from Bangladesh, have been subjected to a hate campaign over the last six months.
In the latest incident, a gang of five men wielding golf clubs broke the windows and dented the bodywork of the sisters' vehicles as they sat watching X Factor on television.
The siblings, who were too scared to give their names, said they were worried the vandalism agai nst their cars would escalate into violent assaults.
Each of the attacks took place in Whitson Place East in Saughton where one of the sisters and her brother live in separate flats.
Police today said they were treating the incidents as "racially motivated" and pledged that they would be "robustly investigated".
The older sister, who is in her 30s, said: "The first attack happened on April 14 when someone poured what seemed to be battery acid on his (her brother] Vauxhall Corsa. It was across the bonnet and the rest of the car, and removed the paintwork. It cost him about £700 to repair.
"Then on October 14, exactly six months later, my Toyota Yaris also had battery acid poured over it. But when I called the police they told me we would need witnesses and suggested we install CCTV."
The family said they had also suffered from racial abuse.
The older sister, who moved to Edinburgh from England five years ago, added: "My sister came round to my flat on Sunday night and parked her Citroen C3 outside my flat. We were watching X Factor when she heard a noise and went out to see what it was.
"She saw around five men wearing hoodies smashing our cars with golf clubs. They had broken the windows and were denting the bodywork.
"My sister shouted at them to stop and her husband tried to run after them. They shouted, "f****** p*** b*******" as they ran off.
"We're very worried about our safety. They've attacked our cars four times but what happens if it escalates and they attack us next? I have an eight-year-old son so I'm worried.
"It's left us very frustrated, stressed and angry. It's pathetic people behind these attacks."
A police spokesman said officers were still investigating the earlier attacks on the family's vehicles.
He added: "Enquiries are ongoing and anyone who witnessed anything suspicious or who has information is asked to contact police immediately."
A 43-year-old man has been arrested with a racially-motivated breach of the peace.
Scotsman
