The second order nonlinear optical response of gold nanoprisms arrays is investigated by means of second harmonic generation (SHG) experiments and simulations. The polarization dependence of the nonlinear response exhibits a 6-fold symmetry, attributed to the local field enhancement through the excitation of the surface plasmon resonances in bow-tie nanoantennas forming the arrays. Experiments show that for polarization of the input light producing excitation of the plasmonic resonances in the bow-tie nanoantennas, the SHG signal is enhanced; this despite the fact that the linear absorption spectrum is not dependent on polarization. The results are confirmed by electrodynamic simulations which demonstrate that SHG is also determined by the local field distribution in the nanoarrays. Moreover, the maximum of SHG intensity is observed at slightly off-resonance excitation, as implemented in the experiments, showing a close relation between the polarization dependence and the structure of the material, additionally revealing the importance of the presence of non-normal electric field components as under focused beam and oblique illumination.