The two 18-year-olds, of Arabian and Pakistani ethnicity, were making their way home in Edinburgh when they were attacked by a gang of youths.
One of the victims was injured as a result of the assault and their home was also damaged.
Police want anyone with information about the hate crime to get in touch.
Police Scotland said the incident happened at around 9pm on Monday in West Pilton Terrace, in the Drylaw area of the city.
The two victims were at the junction with West Granton Road when a group of male youths started shouting racial abuse at them and throwing rocks.
The suspects then chased both victims to their home, before continuing to throw objects at the property, damaging a front window.
Officers are working to identify those believed to be involved and are urging anyone who can help with the investigation to come forward.
Inspector David Happs said: "This incident is being treated as racially motivated.
"Anyone with any further information relevant to this investigation is also asked to contact police immediately.
"Police Scotland is committed to tackling hate crime in all its forms and the local community within Drylaw can rest assured we are devoting appropriate resources to this investigation and offering all the necessary support to both victims."