  We introduce multi-poly-Bernoulli-Carlitz numbers, function field analogues
of multi-poly-Bernoulli numbers of Imatomi-Kaneko-Takeda. We explicitly
describe multi-poly-Bernoulli Carlitz numbers in terms of the Carlitz factorial
and the Stirling-Carlitz numbers of the second kind and also show their
relationships with function field analogues of finite multiple zeta values.
