  We discuss the shuffle product of the Schur multiple zeta values, which are
the special values of Schur multiple zeta functions. We first define
$2$-labeled Schur posets to generalize Yamamoto's integral expression of the
multiple zeta values and consider the product of hook-type Schur multiple zeta
values by using these posets. Then, for the derived terms, we introduce a
modified Hurwitz-type Schur multiple zeta function of hook type, named an
elementary factorial Schur multiple zeta function. Furthermore, we generalize
$2$-labeled Schur posets to consider the shuffle product of the elementary
factorial Schur multiple zeta values and obtain an explicit formula for their
shuffle product.
