The aircraft have brought in medical equipment and food and water supplies from the Red Cross and the UN children's fund (Unicef).
The UN has warned that basic services are unravelling in Yemen, with widespread food and fuel shortages.
Meanwhile, Pakistan has ruled itself out of joining the Saudi-led coalition fighting Houthi rebels in Yemen.
Pakistan's parliament voted against joining its ally, Saudi Arabia, saying in a resolution that it should "maintain neutrality" in Yemen.
The International Committee of the Red Cross (ICRC) said its plane landed in Sanaa carrying 16 tonnes of medical aid, including drugs and surgical equipment.
Unicef's plane has flown in the same amount of aid - bringing food supplements for 20,000 children as well as medical supplies.
"The supplies we have managed to bring in today can make the difference between life and death for children and their families," said Unicef's Julien Harneis.
The arrival of the flights comes after days of delays while both organisations waited for clearance from all sides in the conflict to land in Yemen.
The UN's humanitarian co-ordinator for Yemen has called for a humanitarian "pause" in the bombardment and fighting on the ground to allow the aid to be delivered.
Johannes van der Klaauw told reporters in Geneva that the conflict has now spread to 15 of Yemen's 22 provinces.
He described the situation in Aden in particular as "catastrophic", a descent into urban warfare, with control of the air and seaports shifting daily between rival groups.
A million people in the city risk being cut off from access to clean water within a matter of days unless additional fuel is brought in, he said.
The World Health Organisation (WHO) says almost 650 people have been killed and more than 2,200 have been injured since 19 March, but Mr van der Klaauw said the actual number of casualties is likely to be far higher because many are not being brought to hospital or are being buried immediately.
Yemen has been in chaos since Houthi rebels, backed by army units loyal to the ousted former President Ali Abdullah Saleh, took full control of Sanaa in January and placed current President Abdrabbuh Mansour Hadi under house arrest.
Mr Hadi escaped and took refuge in Aden in February, but left the country at the end of March when the Houthis reached the outskirts of the southern port city.
Saudi Arabia began air strikes two weeks ago against the Houthis, a Zaidi Shia rebel movement that the US and Saudi Arabia allege is receiving military assistance from regional Shia power Iran.
But they have failed to halt the Houthi advance into Aden, as well as neighbouring southern and eastern provinces. Overnight, coalition aircraft targeted the defence ministry building in Sanaa and weapons storage sites.
Saudi Arabia asked Pakistan last month to contribute ships, aircraft and troops to the campaign to restore Mr Hadi to power.
But after days of debate, Pakistan's parliament voted to "maintain neutrality in the Yemen conflict so as to be able to play a proactive diplomatic role to end the crisis".
Analysts say Pakistan, which has a Sunni majority but also a sizeable Shia minority, fears being caught between the two if it sends troops to Yemen.
Who is fighting whom in Yemen?
Houthis - The Zaidi Shia Muslim rebels from the north overran Sanaa last year and then expanded their control. They want to replace Mr Hadi, whose government they say is corrupt. The US alleges Iran is providing military assistance to the rebels.
Ali Abdullah Saleh - Military units loyal to the former president - forced to hand over power in 2011 after mass protests - are fighting alongside the Houthis.
Abdrabbuh Mansour Hadi - The president fled abroad in March as the rebels advanced on Aden, where he had taken refuge in February. Sunni Muslim tribesmen and Southern separatists have formed militia to fight the rebels.
Saudi-led coalition - A US-backed coalition of nine, mostly Sunni Arab states says it is seeking to "defend the legitimate government" of Mr Hadi.
Al-Qaeda in the Arabian Peninsula - AQAP opposes both the Houthis and President Hadi. A rival affiliate of Islamic State has also recently emerged.
Two planes carrying much-needed relief supplies have arrived in the Yemeni capital Sanaa.