  We study the Pieri type formulas for the Schur multiple zeta functions along
with those for the Schur polynomials. To formulate these formulas, we introduce
a new insertion rule for adding boxes in the Young tableaux and obtain the
results for the hook type Schur multiple zeta functions. For the proof, we show
{certain} extended Jacobi-Trudi formulas for the Schur multiple zeta functions.
