The Met Office has announced that up to 15-20mm of rain per hour could fall in some parts of the county.
Thundery showers are expected across parts of Yorkshire, with possible flooding on the roads.
A spokesman for the Met Office said: "An area of rain with possible thundery downpours will continue over parts of central and eastern England on Tuesday with further thundery showers expected to develop to the southeast of this area.
"These will die out for many during Tuesday evening but may persist over Humberside and Lincolnshire coasts into Tuesday night.
"Where the thundery showers develop they are likely to be slow moving hence some areas may miss the showers entirely whilst others could see 2 to 3 hours of heavy rain.
"Where this occurs some disruption is possible such as longer journey times due to flooding of roads and perhaps some flooding of homes and businesses. These impacts will only be localised however.
"An area of showers will spread from the Irish Sea across Wales, and parts of southwest and south England on Tuesday. Whilst many areas will not see the heaviest of these, accumulations of 15-20 mm in an hour are possible along with 30 mm or so in 2 or 3 hours."