Both Jonathan James Nicholson and Mark Alexander Nicholson pleaded guilty to charges relating to their management of Greenway Waste Recycling in Ketley in 2016.
Mark Nicholson, of Keady Road, Armagh, Northern Ireland, and Jonathan Nicholson, of Drumman Heights, Armagh, appeared before Kidderminster Magistrates Court earlier this week.
They both admitted one count of breaching the condition of an environmental permit, between October 12, 2016 and September 17, 2017.
The case was committed to Worcester Crown Court and will be heard on September 1.
Both men were granted unconditional bail.
The Greenway site, at Rock Road, Ketley, was subject to a massive fire earlier this year, with the fire service, Environment Agency and Telford & Wrekin Council spending a month extinguishing the blaze.
More than 1,000 firefighters tackled the incident in April and May.