The area worst affected is expected to be from Shrewsbury south through the county.
While there are no flood warnings - flood alerts mean that low lying roads and farmland could be affected today and into Tuesday.
The government's flood information service said "We expect flooding to affect low lying land and roads adjacent the river from Shrewsbury to Upper Arley. Locations that may be affected are White Abbey, Coalbrookdale, Ironbridge and Bridgnorth."
"We are closely monitoring the situation. Please plan driving routes to avoid low lying roads near rivers, which may be flooded."
There is also a flood alert on the River Teme in South Shropshire.
The flood information service said: "We expect flooding to affect low lying land and roads adjacent the River Teme, River Onny and River Corve and their tributaries. Locations that may be affected include Bishops Castle, Church Stretton, Knighton and Ludlow."