  The multiple zeta values are multivariate generalizations of the values of
the Riemann zeta function at positive integers. The Bowman-Bradley theorem
asserts that the multiple zeta values at the sequences obtained by inserting a
fixed number of twos between 3,1,...,3,1 add up to a rational multiple of a
power of \pi. We show that an analogous theorem holds in a very strong sense
for finite multiple zeta values, which have been investigated by Hoffman and
Zhao among others and recently recast by Zagier.
