One report was by former top officials in the Clinton administration, led by former Secretary of State Madeleine Albright and former Defence Secretary William Perry.
The other, ordered by the Pentagon, has not yet been released however reportedly calls the army "stretched to breaking point".
The first report says the pressure of repeated deployments is corrosive and could have long-term effects on the force.
"While the US military has performed superbly in Afghanistan, Iraq and elsewhere, our ground forces are under enormous strain," it said.
The report says there could be problems in recruiting new troops as well as retaining existing members,
In it, authors accuse the current administration of failing to adequately size and equip the force for the post-invasion occupation of Iraq, saying it has created "a real risk of 'breaking the force.'"
They warn the lack of a credible strategic reserve "increases the risk that potential adversaries will be tempted to challenge the United States".
The document recommends a five-point action plan, including increased funding for the post-Iraq war recovery and greater support for military recruiting and retention efforts.
'Immediate action needed'
The second study, carried out for the Pentagon by military expert Andrew Krepinevich, says the military at its current rate of deployment, may not be able to outlast the insurgency in Iraq, also citing problems in recruitment.
He said the faltering morale amongst overburdened troops and faltering public support for the war could threaten the military's ability to maintain enough forces to see the war through to its end.
The reports warned that immediate action must be taken to repair damaged morale and to make sure Iraqi security forces are ready to assume duties as soon as possible.
But the assessments contrast sharply with the optimism of senior US officials.
Mr Rumsfeld told a press briefing that "this force is not broken", saying the Afghanistan and Iraq invasions displayed the true power of the US military.
"The message from that is not that this armed force is a broken force but that this armed force is enormously capable," he said.
"It is battle hardened, it is not a peacetime force."
Army Secretary Francis Harvey last week said the army was "without a question, the pre-eminent land power in the world."
"Today's army is the most capable, best-trained, best-equipped and most experienced force our nation has fielded in well over a decade," he said.
About 138,000 US troops remain in Iraq, on top of deployments to Afghanistan and Kosovo.