The central belt of Scotland in particular has been badly hit by the high winds and heavy rain, with a total of 23 out of 30 possible train routes affected by a "major disruption."
The storm has caused major line blockages, such as several trees falling onto the line – and overheard wires have also been damaged.
A Tweet posted by the official Network Rail account read: "All services running out of #Edinburgh Waverley & #Glasgow Queen street high level station are currently suspended. This is due to issues & obstructions on various lines at multiple locations. Passengers are advised to consider if their journey is necessary."
A Tweet by the official Scotrail account read: "We’re dealing with severe disruption due to #StormAli right across Scotland. Our advice is Do Not Travel."
Scotrail has also advised passengers that train tickets and smartcards can be used on the following services: First Glasgow, First Bus East, McGills Buses, Stagecoach West, JMB, Whitelaws, Edinburgh Trams, Glasgow Subway, & CityLink between Edinburgh & Glasgow (very limited spaces).
The Met Office issued an amber "be prepared" wind warning for large parts of Scotland which is due to last until 6pm today.
Gusts of up to around 90mph are expected.