The offer is open to those personnel who have a valid pass or are in uniform.
The bus company has also applied poppy artwork – the symbol of remembrance and hope – to 29 of its vehicles throughout the East of Scotland in the run up to Armistice Day.
It also features a message of thanks to the individuals who served and continue to serve.
Douglas Robertson, managing director, Stagecoach East Scotland, said: “We are delighted to once again show our appreciation to those who sacrificed so much.
“This time of year is always a poignant one and it is important that we continue to remember the thousands of men and women who fought for our country.
“We are proud of how many armed force reservists work for Stagecoach and will continue to support them through our pledges with the armed force covenant.”
Stagecoach Group has been a member of the Armed Force Covenant since March 2015, recognising the value of serving personnel, regular and reservists, veterans and military families to both the country and businesses across the country.