Classical molecular dynamics has been performed with explicit polarization on NaOH aqueous solutions from 0.5 mol L$^{–1}$ up to 9.7 mol L$^{–1}$. We adapted a force field of OH$^–$ for polarizable simulation in order to reproduce the NaOH structural and thermodynamics properties in aqueous solutions. A good agreement between theoretical and experimental results has been found. Wide-angle X-ray scattering (WAXS) intensities issued from molecular dynamics are compared to experimental ones measured on Synchrotron facilities. The structure of the first coordination shell of Na$^+$ has been studied to determine the variation of the oxygen number and hydroxide oxygen around the cation. In addition, Na$^+$$–OH^–$ McMillan-Mayer potential issued from molecular dynamics simulations has been calculated and allows for calculating Na$^+$$–OH^–$ pair association constant of 0.1 L mol$^{–1}$, which is in good agreement with the experiments.