Customers hoping to get to Leeds were turned away at Bolton-upon-Dearne, Goldthorpe and Thurnscoe on the first train of the day.
All the seats were taken and other passengers were crammed in along the aisles.
A spokesman for Northern Rail claimed they were aware that there would be an extra demand for tickets due to the Leeds music festival, sold-out cricket test match and Caribbean carnival taking place in the city but they were still unable to provide any extra capacity.
A spokesman for Northern said: “We apologise to customers whose journeys were disrupted on Sunday. We were acutely aware of the events taking place in Yorkshire and worked hard with the available resources to deliver the best possible service.
“Sadly, engineering work, operational difficulties and mechanical issues meant we had fewer carriages than normal and also resulted in some services being cancelled.
“We fully understand the frustration of customers and advise anyone whose journey was impacted by delays or cancellations to apply for compensation via the Delay Repay process which can be found on our website.”