More than 1,000 properties were left without power as gusts reached 79mph (127 km/h), felled trees and caused travel disruption.
Tuesday’s Met Office yellow warning from noon says winds could reach 70mph (113 km/h) in coastal areas with gusts up to 50mph (80 km/h) likely inland.
Heavy rain may be an additional hazard in places, it said.
One lane has been closed on the M48 Severn Bridge due to strong winds during the morning rush hour.
The A55 Britannia Bridge at Anglesey also has restrictions with motorcyclists and drivers towing caravans asked to use alternative routes.
On Monday, Ysgol Bontnewydd Primary School closed due to a power failure after a tree fell on power lines and also hit a car at Bontnewydd, Gwynedd.
Car owner Lowri Pointer explained that a tree opposite her home had been uprooted by the high winds, which had affected power and phone lines in the area.
Western Power Distribution (WPD) said electricity supplies were hit in Newcastle Emlyn and Cardigan in Ceredigion.
SP Energy Network, which manages power in north Wales, said it dealt with problems in Bangor, Treborth, Benllech, Moelfre and Corwen.