Northern services from Leeds to Ilkley and Shipley are being affected by the breakdown.
National Rail said trains may be delayed by up to 30 minutes, or cancelled.
The disruption is expected to continue until at least 8.30pm.
In an update on its website, National Rail said: "Trains may be delayed by up to 30 minutes or cancelled.
"There is no firm estimate yet of how long disruption will last but it is likely to continue until at least 20:30."
Passengers affected by the issue have taken to social media to share their misery.
Hannah Jowett said on Twitter: "@northernassist Last night train home delayed over an hour due to broken train. Tonight I’m stranded at Kirkstall Forge due to broken train. I think you need better trains. #strandedcustomer"
Dylan Meeks said: "@northernassist train (18:26 from Leeds) broken down at Kirkstall Forge. No explanation from driver. And, “No response from control”. What are you doing to get this train moving?"