Two vehicles, a beige-coloured Toyota LandCruiser and a white Mitsubishi Triton, were believed to have left Kalgoorlie-Boulder on Sunday between 10am and 2pm, making for Tjuntjuntjara, Kalgoorlie Police said on Tuesday.
Both vehicles contained elderly drivers, with the Mitsubishi Triton also containing five other passengers, four of whom are children aged between seven and 17.
"Concerns are held for the occupants of these two vehicles due to serious weather conditions. It is unknown how much food and water the occupants have in their possession," police said in a statement.
Parts of WA experienced more than half a year's rain in 24 hours over the weekend, with more than 155mm of rain recorded at Rawlinna, 900km east of Perth, since 9am Friday.
The Eyre Highway has been closed since the weekend and is likely to remain out of operation for several days.
The Trans-Australian Railway line has also been affected, with key freight routes running between WA and South Australia through the Nullarbor closed amid the rain.
The Bureau of Meteorology forecast totals of up to 130mm for parts of the Goldfields, Eucla and south interior districts on Tuesday.
Average rainfall for the area is about 260mm a year, with the resulting downpours wreaking havoc with transport routes.
Flooding had affected large parts of the Eastern Goldfields, the central parts of the Eucla districts and much of the interior region around there, with many communities affected.
The rain came after a cold front moved across the south-west of WA on Saturday, and it brought significant moisture from the tropics to the eastern goldfields and interior of the state.
WA's Department of Fire and Emergency Services issued a warning to residents in Carnegie, Rawlinna, Cocklebiddy and Eyre to seek shelter, stand clear of windows and refrain from driving through flood waters.
"This is not typical weather for south-eastern Western Australia," DFES said.
"If you live in parts of the Goldfields, Eucla and South Interior districts you should take action and stay safe with severe weather to come."
The DFES deputy assistant commissioner, Gary Gifford, told ABC Regional Drive the highway was expected to remain closed until the end of the week.
"With the forecast which the [Bureau of Meteorology] has provided us with regard to the unprecedented weather which is coming through the southern interior at the moment, we're certainly planning towards three and five days at this point of view."
The BoM senior meteorologist Joey Rawson said records had been "smashed" amid the downfall.
"We've just seen consecutive days of significant rainfall through that area. The 141mm that we had on Sunday just smashed any previous record at Eyre."
Rawson said the previous record at Eyre, just south of Madura, was 81.2mm, which was recorded in 2011.
"This is an unprecedented event of heavy rainfall, and it is due to continue as well, we could see another 100mm in that area over the next 24 hours."
Rawson said this was a "unique weather event" with many of the communities there rarely facing flooding this severe.
"The highway hasn't been closed, completely closed, for a long time," he said.
"Usually they still allow transport trucks to go through if there's a smoke event, but it hasn't been completely closed for many years."
While it was uncertain how long the flooding would remain, the rain was due to ease later in the week, with the rain band expected to move on by Thursday or Friday.
Meanwhile, Christmas Island could be facing a tropical cyclone in the coming days, as a tropical low in the Indian Ocean tracks closer to the Pilbara.
The low is expected to develop into a cyclone later this week, with the possibility it will bring gale force winds to Christmas Island as it passes.
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