The three soldiers killed on patrol in Helmand Province were understood to have been travelling in a heavily armoured Mastiff vehicle when it was hit by a roadside bomb.
The tank, which is strengthened by heavy grids which cause anti-tank weapons to detonate further from the body of the vehicle, was deployed in 1999 to combat the threat of IEDs (improvised explosive devices).
No troops had died in the vehicle prior to the deadly attack on The Royal Highland Fusiliers, 2nd Battalion The Royal Regiment of Scotland.
Former Army chief of staff Lord Dannatt told Radio 4's Today programme: "The Taliban have found a way of countering the protective qualities and characteristics of the Mastiff."
He said he understood the IED "may well have physically lifted up the vehicle and possibly even turned it over."
Poppyscotland, which raises funds to support ex-servicemen and women, has said its members are "deeply saddened" by the deaths of three British soldiers in Helmand Province.
A posting on its Facebook page read:
We're deeply saddened to hear that three members of the Royal Highland Fusiliers, the 2nd Battalion The Royal Regiment of Scotland have been killed in Afghanistan. Our thoughts are with their families and colleagues.
– Scotland's First Minister Alex Salmond
This is tragic news and our thoughts and deepest sympathies are with the families and loved ones of the soldiers who have been lost.
This incident demonstrates once again the dangers faced by our armed forces, often on a daily basis, and they deserve our deepest gratitude and respect for the job they do in some of the most difficult and trying circumstances imaginable.
No words can truly bring comfort to the families at a time like this, but the thoughts and prayers of everyone in Scotland will be with them upon hearing this dreadful news.
Tragic news from Afghanistan. My thoughts and condolences are with the families and friends of those killed.
Six soldiers were injured in the roadside bomb attack that killed three soldiers from The Royal Highland Fusiliers, 2nd Battalion The Royal Regiment of Scotland.
The Prime Minister admitted the UK has "paid a very high price for the work we are doing in Afghanistan" after three British soldiers were killed in a roadside bomb attack.
The deaths take the number of UK service members who have lost their lives since operations in Afghanistan began in October 2001 to 444.
David Cameron told ITV's Daybreak: "We have paid a very high price for the work we are doing in Afghanistan.
"It is important work because it is vital that that country doesn't again become a haven for terrorists, terrorists that can threaten us here in the UK but today our thoughts should be with the families and friends of those that have suffered."
The three soldiers killed in Helmand Province came from The Royal Highland Fusiliers, 2nd Battalion The Royal Regiment of Scotland (commonly referred to as 2 SCOTS).
According to the Ministry of Defence's Army website, around 350 soldiers from 2 SCOTS deployed to Afghanistan throughout March for a six-month operational tour.
The battalion, which is based in Penicuik near Edinburgh, were sent over to take on a variety of roles, including advising and training the Afghan National Security Forces, as part of Task Force Helmand.
The killing of three British soldiers in Helmand Province has taken the UK's death toll from operations in Afghanistan, which began in October 2001, to 444. Six have died this year.
The latest deadly attack came on the third day of the Taliban's self-proclaimed "spring offensive".
The soldiers, from The Royal Highland Fusiliers, 2nd Battalion The Royal Regiment of Scotland, were on routine patrol in Nahr-e Saraj district when their vehicle was hit by an improvised explosive device.
They received immediate medical attention and were evacuated by air to the Military Hospital at Camp Bastion but could not be saved, the MoD said.
Other blasts throughout the country killed nine civilians and a police commander.
– Ministry of Defence spokesman
Our thoughts are with the families who have lost loved ones in this incident, which underlines the threats faced by our personnel as they continue to hand over security operations to their Afghan counterparts ahead of UK combat operations concluding by the end of next year.
Security in Helmand, where most UK forces are based, is steadily improving with Afghan forces already responsible for the bulk of the province - but the environment in which our troops operate remains risky and dangerous, including the threat of improvised explosive devices and insurgent attack.