The alerts mean that flooding is possible and people living in those areas should prepared for potential flooding.
It follows a weather warning about possible flash floods, hail and violent thunderstorms in the region today and tomorrow.
Issuing the flood alerts, the Environment Agency said: "During today and into the early hours of Friday there is the potential for localised and very heavy thunderstorms to affect widely scattered localities across South and West Yorkshire.
"It is not possible to predict the precise location of these thunderstorms, but where they occur there’s a risk of localised flooding of roads, homes and businesses.
"The uncertainty over where it will fall means that we are taking the precautionary measures and our staff continue to monitor the situation from the incident room and our field teams are working with partners to ensure that defences are clear of obstructions."
There are currently 35 flood alerts in England, including:
Leeds and West Yorkshire
Ings Beck catchments including Oakenshaw Beck
Meanwood Beck, Wyke Beck and Wortley Beck catchments
River Calder upper catchments
River Spen and Batley Beck catchments
Wash Dike catchment
Earby Beck and Glusburn Beck catchments
Upper River Nidd
Upper River Swale
Upper River Ure
Upper River Wharfe
Sheffield and South Yorkshire
Blackburn Brook catchment
River Sheaf and Porter Brook
Whiston Brook catchment