Like all sauropods, Rinconsaurus was a large long-necked quadrupedal animal, with a long, whip-like tail and four pillar-like legs.

The fossils, which consisted of three individuals (two adults and one juvenile), were excavated by Jorge Calvo of the Paleontology Museum of the National University of Comahue.

[1] The type, and only known species, Rinconsaurus caudamirus, was described by Calvo and Bernardo J. González Riga of the Paleovertebrate Laboratory in Mendoza, Argentina, in 2003.

The authors noted derived traits unique to the genus, including distinctive tail vertebrae with bony processes.

The generic name refers to Rincón de los Sauces, where the fossils were discovered, while the specific name, caudamirus, means "amazing in the tail" in Latin, in reference to the unusual shape of the tail vertebrae, especially a strange sequence of procoelous, amphicoelous, opisthocoelous, biconvex and ultimately again procoelous vertebrae shown by one individual.