Large parts of the county are included in the yellow warning, including Sheffield, Doncaster, Bradford, Leeds and Harrogate, but the East Coast and York itself come just outside of the zone expected to be affected.
The warning is in place until 10pm today (Friday) with another warning returning on Saturday between 11am and 9pm.
Flooding, lightning strikes and hail are all included in the experts' warning with warnings about power cuts and as well as disruption to public transport.
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The Met Office website warns: "Homes and businesses could be flooded, causing damage to some buildings.
"Fast flowing or deep floodwater is possible, causing a danger to life.
"Spray and flooding could lead to difficult driving conditions and some road closures and where flooding and lightning strikes occur, there is a chance of delays and some cancellations to train and bus services.
"Some communities may be cut off by flooded roads.
"Possible power cuts and loss of other services to some homes and businesses."