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A parameterization of the nucleon-nucleon elastic scattering amplitude isneeded for future experiments with nucleon and nuclear beams in the beammomentum range of 2 -- 50 GeV/c/nucleon. There are many parameterizations ofthe amplitude at $P_{lab} >$ 25--50 GeV/c, and at $P_{lab} \leq$ 5 GeV/c. Ourpaper is aimed to cover the range between 5 -- 50 GeV/c.  The amplitude is used in Glauber calculations of various cross sections andMonte Carlo simulations of nucleon-nucleon scatterings. Usually, thedifferential nucleon-nucleon elastic scattering cross sections are described byan exponential expression. Corresponding experimental data on $pp$ interactionsat $|t|>$ 0.005 (GeV/c)$^2$ and $|t|\leq$ 0.125 (GeV/c)$^2$ have been fit. Wepropose formulae to approximate the beam momentum dependence of theseparameters in the momentum range considered. The same was done for $np$interactions at $|t|\leq$ 0.5 (GeV/c)$^2$. Expressions for the momentumdependence of the total and elastic cross sections, and the ratio of real toimaginary parts of the amplitude at zero momentum transfer are also given for$pp$ and $np$ collisions. These results are sufficient for a firstapproximation of the Glauber calculations. For more exact calculations we fitthe data at $|t|>$ 0.005 (GeV/c)$^2$ without restrictions on the maximum valueof $|t|$ using an expression based on two coherent exponential. The parametersof the fits are found for the beam momentum range 2 -- 50 GeV/c.

Empirical Parameterization of Nucleon-Nucleon Elastic Scattering Amplitude at High Beam Momenta for Glauber Calculations and Monte Carlo Simulations