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.
Police said they are following a positive line of inquiry but want anyone with information about the hate crime to get in touch.
Police Scotland said the incident happened at around 9pm yesterday 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 and stones in their direction.
The suspects then chased both victims.
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: "As a result of being struck by rocks, one of the victims suffered an injury to his arm. We are undertaking a thorough inquiry to bring those responsible to justice.
"This incident is being treated as racially motivated and we are keen to hear from anyone who was in the West Pilton Terrace area on Monday evening and witnessed the disturbance or who saw anything suspicious.
"In addition, 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."
Police can be contacted on 101, while the charity Crimestoppers can be reached on 0800 555 111.