Fears had arisen that insurers would claim the impact of former Hurricane Ophelia was an "act of God" and refuse to pay out.
But Insurance Ireland, the umbrella body for the industry, said motor insurance cover operates as normal during and after the storm.
"This is not impacted by the weather conditions," a spokesman said.
Damage to cars caused by the storm is covered by comprehensive motor insurance policies.
Third party fire and theft policies cover motorists for damage to other cars in the event of an accident, injury to other people, or damage to your car in the event of a fire or theft.
And household buildings and contents insurance policies will cover damage caused by storms.
Insurers will usually pay for the cost of temporary repairs, the insurance representative body said.
Householders were advised to keep receipts.
A spokesman added: "Insurers will also usually pay for the cost of alternative accommodation, if the home becomes uninhabitable."
Householders were told to check the full extent of their policies and contact their insurer or broker after the event, if there is damage.
And it added: "Insurance Ireland advises motorists to heed the warnings in place from the authorities and avoid all non-essential travel."
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