The lawsuit was filed Friday after the state executed 63-year-old Edmund Zagorski the night prior. Zagorski had requested the electric chair in place of a lethal injection of chemicals.
Many executions conducted by lethal injection over the past few years have been botched as states scramble to find drugs to replace the ones that manufacturers have withheld for their use in capital punishments.
Zagorski's lawyers argued that electrocution was more humane than the three-drug cocktail used in Tennessee, which has been condemned as a form of torture by some experts, according to NPR.
The Supreme Court had thrown out Zagorski's appeal in which he had asked for a ruling on the constitutionality of him being forced to choose between lethal injection and electrocution.
The four inmates even picked a place where they would like to be shot to death. "The suit says that Big Buck Shooting Range, on the grounds of Riverbend Maximum Security Institution, can 'easily accommodate what little equipment is required for an execution by firing squad," the Nashville Tennessean reported.
Only Mississippi, Oklahoma and Utah allow for firing squad executions, but they are not typically used.