  In this paper we want to study the non-Kodaira fibres in a smooth
equidimensional elliptic threefold. If the morphism to the Weierstrass model of
the fibration is crepant, then we can locate the non-Kodaira fibres and give a
description of their structure. In particular, they lie over the singular
points of the (reduced) discriminant of the fibration and are contraction of a
Kodaira fibre, whose type can be predicted using Tate's algorithm.
