Firefighters say they were called out to around 20 flooding incidents in the Llanelli, Kidwelly and Cross hands areas where domestic properties were affected.
Some roads in Carmarthenshire which were closed because of flooding are now passable after the heavy rain.
Train services between Cardiff and Bridgend were disrupted overnight and buses replaced trains between Newport and Ebbw Vale Parkway. Services are back to normal.
The rain eased in the early hours.
The Environment Agency has 9 flood alerts in force.