The insurer advises that people should ensure their pets are in a safe place and cannot escape if frightened by noise.
Other suggestions include playing music or putting the television on to drown out sudden noises, and exercising dogs before dark.
RIAS managing director Janet Connor said: "Fireworks can be very scary for pets, large and small and we strongly recommend pet owners take heed of the advice of specialist organisations like the RSPCA and the PDSA in order to minimise the risk to their pets."
Meanwhile, the Co-Operative supermarket is teaming up with the RSPCA to distribute a new leaflet to give pet owners practical advice on using sound therapy to overcome their dogs' fear of loud noises.
It is estimated that nearly half of dogs show signs of fear when they hear fireworks.
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