Tannudiscus Pokrovskaya (1959) is a genus of eodiscinid trilobites belonging to the family Weymouthiidae Kobayashi T. (1943), Order Agnostida (Salter 1864). It lived during the late Lower Cambrian, with remains found in Canada (Newfoundland), China (Gansu), The United Kingdom (England), and the Russian Federation (Tuva, Gorno-Altayskaya).

TYPE SPECIES: T. tannulaicus Pokrovskaya, 1959.

The Weymouthiid family shows a trend of shortening the occipital ring. In Chelediscus and Tannudiscus the occipital ring is entirely obliterated as in the Agnostina suborder. Tannudiscus has some other characters it shares with the Agnostina, such as a glabella consisting of two lobes and the occipital ring divided into basal glabellar lobes. Both the glabella and pygidial axis are isolated from the border furrow, and the latter is undivided. It is therefore considered likely that the Agnostina descended directly from a species assignable to Tannudiscus. The earliest known Agnostina is Archaeagnostus (Peronopsidae). According to Cotton and Fortey (2005) Tannudiscus is polyphyletic.

Tannudiscus lacks eyes and has a thorax of three segments. The glabella almost touches the anterior border and consists of two inflated lobes, the frontal one slightly wider than the posterior lobe—a characteristic that is further developed in the Condylopygidae. Posterior glabellar lobe lacks a spine. The occipital ring is formed into two basal lateral lobes. The border is convex, moderately wide, more so in front of the glabella and extends to rear of the glabella in some species. Pygidial axis is conical, with seven or eight rings, and may or may not reach posterior border furrow. The furrows defining the axial rings are indistinct or obsolete. Pygidial border is almost flat, but similar in width to the cephalic border.