  We study the formality of orientable sphere bundles over connected compact
manifolds. When the base manifold is formal, we prove that the formality of the
bundle is equivalent to the vanishing of the Bianchi-Massey tensor introduced
by Crowley-Nordstr\"{o}m. As an example, this implies that the unit tangent
bundle over a formal manifold can only be formal when the base manifold has
vanishing Euler characteristic or a rational cohomology ring generated by one
element. When the base manifold is not formal, we give an obstruction to the
formality of sphere bundles whose Euler class is reducible.
