The fire at M & R Commercials in Felinfach Industrial Estate, Fforestfach, started at about 06:00 BST on Monday.
Residents are being told to keep doors and windows shut and to keep away from the immediate vicinity of the incident.
Trains between Swansea and Llanelli on the south Wales mainline are disrupted.
Mid and West Wales Fire Service have established an incident command unit at the scene and say there are 10 major pumping vehicles and special appliances at the scene.
A spokesman said they had made "significant progress" in controlling the fire, but crews would remain on site for the rest of the day "dampening down and liaising with partners on returning the site to normal operation".
He said there was no current risk to local residents or commercial premises, and police were continuing to maintain cordons for the duration of the incident.
The main railway line has been reopened but passengers could face residual delays.
An Arriva Trains Wales spokesman said: "Trains are proceeding at caution, however, disruption may last some time with the knock on effect this has had on services."
Natural Resources Wales will investigate the incident and advised M & R Commercials to "further reduce the impact of the fire".
"Our operational team have installed booms to reduce the impact of contaminated water entering the Fforestfach Stream," Jonathan Jones, NRW lead for the incident, said.
"Our air quality expert is working with Public Health Wales and the local authority to manage the risks to air quality.
"We are investigating and advising to protect the environment and the local community from pollution caused by the fire."
Roads around the industrial estate are also closed and South Wales Police is advising people to avoid the area.
About 70 firefighters are tackling a major blaze at a recycling unit in Swansea where 4,000 tyres, cylinders, waste and scrap vehicles are alight.