  Let $E_{1},...,E_{m},F$ be Banach spaces. The index of summability of
$\left(E_{1}\times\cdots\times E_{m},F\right) $ is a kind of measure of how far
the $m$-linear operators $T:E_{1}\times\cdots\times E_{m}\rightarrow F$ are
from being multiple summing. In this paper we estimate the index of summability
of several pairs of Banach spaces$.$
