An issue with overhead wiring led to widespread disruption after the problem was discovered at 7am with five platforms affected.
The fault has hit services running to Aberdeen, Edinburgh and Inverness with a number of local routes also being affected.
Train cancellations were announced on the Cathcart Circle, Newton, Neilston and Kilmarnock with services to Clarkston, East Kilbride, Cambuslang and Motherwell also disrupted.
ScotRail has arranged replacement bus services for some of the routes affected with the disruption expected to last until noon.
A ScotRail spokesperson said: “There are overhead wire problems which are affecting access to five platforms. Engineers are on site to diagnose and repair. It’s not possible to say how long disruption to services will last.”
“Customers should retain their tickets as the nature of this disruption means they may be entitled to compensation through our Delay Repay scheme.”