Flowering occurs from June to July and is followed by fruit which are dry, almost spherical, 6–7.5 mm (0.2–0.3 in) long and have a glabrous, papery covering.

[2][3] Eremophila undulata was first formally described by Robert Chinnock in 1980 and the description was published in Journal of the Adelaide Botanic Garden.

[4][5] The type specimen was found by Alex George in 1974, 88 km (50 mi) south of Neale Junction in the Great Victoria Desert.

[2] This eremophila is only known from a few small areas north of Rawlinna in the Great Victoria Desert biogeographic region[7][8] near where the type specimen was found.

[2][3] Eremophila undulata is classified as "Priority Two" by the Western Australian Government Department of Parks and Wildlife[7] meaning that is poorly known and from only one or a few locations.