Virtus, which is replacing Osprey armour, is described by the Ministry of Defence (MoD) as "one of the most advanced integrated body armour and load carrying systems in the world".
But among other complaints, soldiers say its webbing - where ammunition and kit is stored - has been snapping.
The MoD said it was working with the armour's supplier to make improvements.
Virtus body armour was first rolled out at the beginning of the year and is gradually replacing Osprey armour in phases.
So far around 9,000 units of Virtus body armour, helmets and load-carrying systems have been issued to a number of units - including members of the Parachute Regiment, the Rifles, Royal Marines and Royal Artillery.
The main advantage of the Virtus system is that it is lighter.
But soldiers have said it gives limited space for extra equipment - such as radios and medical supplies - and that if soldiers go to ground with it they find it hard to get back up.
"Daysack and Bergen should be used as fire fuel" is one of their comments on social media.
Others said: "Just about room for a Mars bar and biscuits" and "Snapping!"
The Virtus system is 4.7kg (10.4lb) lighter than the older Osprey body armour and will become even lighter when new armour plates are issued.
There are good reasons to ease the burden.
In Afghanistan a British soldier on patrol could be carrying loads of around 22kg (50lbs).
The Taliban would often refer to them as "tortoises" or "camels" on their radios as the British soldier nearly buckled under the weight.
These heavy loads made it more difficult to move "tactically" and could contribute to muscular/skeletal  injuries.
The likelihood that women will soon be allowed to serve alongside men in close combat roles is another reason to address the issue surrounding weight.
The most radical innovation of the new Virtus kit is an integral spine, known as the dynamic weight distribution system.
It is linked to the wearer's waist belt and helps spread the load across their back, shoulders and hips.
Instead of the old Velcro straps, there is a quick release pin - a bonus when soldiers need to ditch their equipment to fight.
The new helmet is also lighter.
Virtus is also "modular" - so pouches can easily be added or subtracted.
The father of one serving soldier issued with the equipment got in touch with the BBC to complain.
He said he was "appalled" that soldiers were being issued with what he considered to be "sub-standard kit" and hoped the British Army had learned from the lessons of the past.
He said his son and his comrades had found it all but impossible to get back on their feet when they went to ground wearing the new system - making life difficult for an infantry soldier.
They were also unable to squeeze all their equipment into the new Bergen rucksacks and had trouble putting the armour on in the dark, he said.
The MoD said: "As with every new system there have been some issues during the initial roll out, and, as a result of constructive feedback from our troops, we are working with our supplier to make improvements."
The MoD added that the  supplier of the system, an Israeli company, was required to address any problems as  as part of the Â£14.6m contract.
British army soldiers have raised concerns about their new body armour, the BBC has learned.