  Recently, several people study finite multiple zeta values (FMZVs) and finite
polylogarithms (FPs). In this paper, we introduce finite multiple
polylogarithms (FMPs), which are natural generalizations of FMZVs and FPs, and
we establish functional equations of FMPs. As applications of these functional
equations, we calculate special values of FMPs containing generalizations of
congruences obtained by Me\v{s}trovi\'c, Z. W. Sun, Z. W. Sun-L. L. Zhao, and
Tauraso-J. Zhao. We show supercongruences for certain generalized Bernoulli
numbers and the Bernoulli numbers as an appendix.
