Amber warnings for rain until late this afternoon have been issued by the Met Office up and gusts of wind up to 58mph are expected in parts of Strathclyde.
After the heavy rain passes tonight, a band of lighter rain will follow right behind it, according to forecasters.
However, this morning's weather was not as bad as expected, according to Transport Minister Keith Brown.
Last night he had warned commuters to prepare for a rough morning, but this morning he said the weather at the start of the rush hour was "slightly better perhaps than was expected".
He said: "We expect further rain to come across from Northern Ireland, and are seeing some flooding and one or two trees coming down.
"It is perhaps not as bad as we had expected and we will have to wait to see what the rest of the day brings."
On the M8 in Renfrewshire, near Glasgow Airport, surface water caused queues during the morning rush hour in both directions between Junction 29 St James and Junction 27 Arkleston.
And, at around 9am, flooding caused hazardous driving conditions on the A82 Dumbarton Road in Bowling. The problem had cleared by 10am, but motorists were warned to take care on the roads.
On the M73 in South Lanarkshire, flooding at Junction 1 southbound led to the closure of one lane on the slip road at around 10am.
And on the M74, also in South Lanarkshire, one lane was closed southbound at Junction 4, Maryville, because of flooding just after 10am.
On the railways, flooding on the line caused cancellations and delays between Kilmarnock and Dumfries.
The Met Office's Dan Williams said: "When this intense weather front has moved through, which it will have done by this evening, there will be a band of lighter rain right behind it.
"It will stay wet and windy for the rest of today with up to 40mm of rain falling in some places.
"Tomorrow will see a mix of sunshine and showers for Glasgow and the west, with some bright spells throughout the day.
"Saturday will be quite nice to start with, bright and mainly dry.
"But by Saturday evening a band of low pressure will come in and that will bring with it rain and winds.
"Things will be unsettled on Sunday unfortunately."