Euconcordia is an extinct genus of Late Carboniferous captorhinid known from Greenwood County, Kansas of the United States.

It was collected in the Hamilton Quarry, from the Calhouns Shale Formation of the Shawnee Group, dating to the Virgilian stage (or alternatively late Kasimovian to early Gzhelian stage) of the Late Pennsylvanian Series, about 300 million years ago.

The original generic name was derived from the Latin concordia, meaning "unity" or "harmony".

The specific name honors Christopher R. Cunningham for studying this taxon as part of his PhD thesis on the Hamilton Quarry.

[1] The original generic name turned out to be preoccupied by extant hippolytid crustacean Concordia Kingsley, 1880 (currently considered a junior synonym of Latreutes Stimpson, 1860).