Speaking to the Yorkshire Evening Post, the trust said the tyres had been dumped on the Brockadale nature reserve in Pontefract earlier this week.
The trust said: "As a charity, removing them will cost us time and money we don't have, impacting our vital work for wildlife and nature.
"The tyres were dumped earlier this week and there around 1000 of them."
The trust said they are working with Selby District Council and the police to try and find out who left them.
Yorkshire Wildlife Trust added: "We've seen an incredible amount of support on Facebook so far - it's great.
"We're looking into the options available for removal and recycling at the moment while the police investigate.
"Any donations are appreciated at https://www.ywt.org.uk/support-us/donate."