  In this work, numerical simulations were used to investigate the
gravitational stochastic background produced by coalescences occurring up to $z
\sim 5$ of double neutron star systems. The cosmic coalescence rate was derived
from Monte Carlo methods using the probability distributions for forming a
massive binary and to occur a coalescence in a given redshift. A truly
continuous background is produced by events located only beyond the critical
redshift $z_* = 0.23$. Events occurring in the redshift interval $0.027<z<0.23$
give origin to a "popcorn" noise, while those arising closer than $z = 0.027$
produce a shot noise. The gravitational density parameter $\Omega_{gw}$ for the
continuous background reaches a maximum around 670 Hz with an amplitude of
$1.1\times 10^{-9}$, while the "popcorn" noise has an amplitude about one order
of magnitude higher and the maximum occurs around a frequency of 1.2 kHz. The
signal is below the sensitivity of the first generation of detectors but could
be detectable by the future generation of ground based interferometers.
Correlating two coincident advanced-LIGO detectors or two EGO interferometers,
the expected S/N ratio are respectively 0.5 and 10.
