The Met Office has issued a yellow weather warning and told people to take extra care around the seafront areas along the Yorkshire coast.
It said strong northwesterly winds are expected during Tuesday night and Wednesday with possible transport disruption.
The warning runs from 9pm on Tuesday until 3pm on Wednesday.
The Met Office said there could be gusts of up to 50mph, which could affect public transport services, cause delays for high-sided vehicles on exposed routes and bridges and possibly lead to power cuts.
"It's likely that some coastal routes, sea fronts and coastal communities are affected by spray and/or large waves," it added.
Tuesday is likely to have a wet start and although it will become drier as the day progresses, the wind is likely to pick up. Wednesday will be dry with temperatures up to around 10C.