  A parameterization of the nucleon-nucleon elastic scattering amplitude is
needed for future experiments with nucleon and nuclear beams in the beam
momentum range of 2 -- 50 GeV/c/nucleon. There are many parameterizations of
the amplitude at $P_{lab} >$ 25--50 GeV/c, and at $P_{lab} \leq$ 5 GeV/c. Our
paper is aimed to cover the range between 5 -- 50 GeV/c.
  The amplitude is used in Glauber calculations of various cross sections and
Monte Carlo simulations of nucleon-nucleon scatterings. Usually, the
differential nucleon-nucleon elastic scattering cross sections are described by
an exponential expression. Corresponding experimental data on $pp$ interactions
at $|t|>$ 0.005 (GeV/c)$^2$ and $|t|\leq$ 0.125 (GeV/c)$^2$ have been fit. We
propose formulae to approximate the beam momentum dependence of these
parameters in the momentum range considered. The same was done for $np$
interactions at $|t|\leq$ 0.5 (GeV/c)$^2$. Expressions for the momentum
dependence of the total and elastic cross sections, and the ratio of real to
imaginary parts of the amplitude at zero momentum transfer are also given for
$pp$ and $np$ collisions. These results are sufficient for a first
approximation of the Glauber calculations. For more exact calculations we fit
the data at $|t|>$ 0.005 (GeV/c)$^2$ without restrictions on the maximum value
of $|t|$ using an expression based on two coherent exponential. The parameters
of the fits are found for the beam momentum range 2 -- 50 GeV/c.

High Energy Physics - Phenomenology;High Energy Physics - Experiment;Nuclear Experiment;Nuclear Theory