  The concept of tensor rank, introduced in the twenties, has been popularized
at the beginning of the seventies. This has allowed to carry out Factor
Analysis on arrays with more than two indices. The generic rank may be seen as
an upper bound to the number of factors that can be extracted from a given
tensor. We explain in this short paper how to obtain numerically the generic
rank of tensors of arbitrary dimensions, and compare it with the rare algebraic
results already known at order three. In particular, we examine the cases of
symmetric tensors, tensors with symmetric matrix slices, or tensors with free
entries.
