The delays and cancellations affecting 20 lines are expected to continue until the end of the day, the ScotRail Alliance with Network Rail warned travellers.
Routes hit included the main link between Edinburgh and Glasgow, where trains were cut to half-hourly frequency.
However, the widespread impact of the disruption stretched as far as Aberdeen and Inverness, and to Dumbarton and Lanark.
It was caused by three separate signalling faults and a burst water main.
The first fault, to a train axle counter in the Queen Street tunnel in Glasgow early this morning, affected most trains using the main station.
It coincided with the burst main, which caused water to leak into a tunnel onto overhead electric wires at Kirkhill in South Lanarkshire.
The problems were followed by telecommunication faults with signalling around 1pm at Greenhill junction, near Croy in North Lanarkshire, and Newton in South Lanarkshire.
The telecomms faults are still being fixed but it is not known if they are connected.
The alliance said all routes in and out of Queen Street were being disrupted apart from to Anniesland and Oban/Mallaig.
Others affected are Glasgow-Edinburgh via Shotts, Dalmuir to Motherwell via Whifflet, Milngavie to Motherwell/Cumbernauld via Blantyre, Glasgow Central to Lanark and Glasgow Central to Newton via Kings Park.
Passengers can use First and JMB bus services instead.
Scottish Labour transport spokesman Colin Smyth said: “These disruptions and delays are yet another kick in the teeth for Scotland’s hard pressed rail passengers.
“This is the last thing they need at a time they are suffering from missed stops, overcrowded trains and fares that are rising above their wages.”
An alliance spokesperson: “Due to two separate signal faults, a number of our services will be subject to disruption.
“We know how frustrating this is for our customers and are doing everything we can to get things back to normal.
“We are encouraging customers to download our app, or check @ScotRail on Twitter, for the most up to date information.
“Customers travelling between Edinburgh and Glasgow should consider travelling on the Queen Street low level line via Airdrie.
“Customers delayed by 30 minutes or more are entitled to compensation under our Delay Repay scheme.
“Customers can claim this by keeping hold of their tickets and visiting our website.”