The ground above more than 250 graves in Selby Cemetery has begun to sink by depths of up to two feet because of the floods.
But Selby District Council in charge of maintaining the cemetery has assured families that the problem will be sorted out within a month.
Coun Steve Shaw-Wright said the earth covering the graves had begun to subside as water drained from the soil, leaving the ground resembling a hollowed-out coffin.
A project costing between £2,500 and £3,000 is being implemented by the district council to restore the grave plots.
More than 30 tons of topsoil will be used in the operation.
Coun Shaw-Wright said: "This is just another fall-out from the floods.
"We are asking families to remain patient and not to try to do the work themselves. We hope to complete the work within a month."
selby@ycp.co.uk
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