Guards and retail and revenue staff voted by more than seven to one to take action after rejecting a 3.6% pay offer, which is below inflation.
Three separate 24-hour strikes have been set for 30 July, 13 and 27 August.
Bob Crow, RMT general secretary, said members had made it clear to Silverlink that they were not prepared to accept what amounts to a pay cut.
He said: “This isn’t just the worst pay offer in the industry this year, it is also way below the offers they have made to other members of their own workforce. If Silverlink want to avoid strike action they should acknowledge our members’ anger, get real and sit down with us to negotiate a sensible pay deal.”