Authorities say more than 18 people were killed in the capital, Hanoi, where many of the streets remain under water.
Forecasters say more rain is expected through Tuesday. Parts of the country have seen more than 30 centimeters of rain in a single day.
In China, officials say 26 people were killed, and 41 were reported missing, after heavy rains caused a series of mudslides in the country's southwest Yunnan province.
Authorities say more than 410,000 people have been affected by the weather. The official Xinhua news agency reports that 1,000 homes have collapsed and more than 2,300 were damaged.