24 people were killed in northern Yemen, while 18 lives were lost in Saudi Arabia in flooding caused by heavy rains, the officials said.
Security sources said 10 people died in the province of Amran, north of the Yemeni capital Sanaa, and more people were missing.
Flooding damaged several houses and cut off roads in both Amran and Hajjah, northwest of Sanaa, where 14 people were killed, some of them in landslides.
In Saudi Arabia, 18 people were killed in heavy rains during the past week, the civil defence agency said.
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In a statement, it said the toll covered much of the country, from Riyadh to Hail, Mecca, Medina, Al-Baha, Asir, Najran and Jazan.
The agency said it rescued 915 people.
Among the dead were two people in the southwestern Jazan region, which borders Yemen.
The pair died when three areas in the mountainous district were inundated by flood waters, Al-Ekhbaria news channel reported on its Twitter feed.
Another 27 people in Al-Baha were injured over three days because of accidents during heavy rains
Severe downpours have struck Saudi Arabia this week, including in the desert capital Riyadh where schools closed on yesterday after floods caused traffic chaos during a storm.