The elastic and kinetic properties of liquid nitrogen have been calculated using Molecular Dynamics (MD) computer simulations. The interactions of the atoms were approximated by the Lennard-Jones (LJ) pair potential. Shear modulus (coefficient of rigidity), bulk modulus (inverse isothermal compressibility), shear waves speed and kinetic properties (work done by a diffusing atom) were calculated by analytic expressions using direct simulation data for the thermodynamic quantities. The thermodynamic quantities are pressure and internal energy. The shear modulus and bulk modulus decrease as temperature increases but increase with density. The speed of the shear waves generated in nitrogen decreases as investigated density decreases. The work done by a diffusing atom of nitrogen also decreases with density. Elastic and kinetic properties of nitrogen are directly proportional to density making the properties to be more pronounced in solid state. The shear modulus ranges from 0.63GPa to 1.37GPa while the bulk modulus ranges from 1.02GPa to 2.44GPa at the investigated temperatures and densities. At temperature of 20K, the bulk modulus of solid nitrogen compared well with experimental values with small discrepancy.