For parameterization deuteron wave functions as a product of exponential function rⁿ by the sum of the exponential terms Ai*exp(-a_i*r²) are received analytical forms for spherical S₀ and quadrupole S₂ deuteron form factors. The modern status of experimental data for deuteron tensor polarizations t₂₀ and t₂₁ is analysed. On received analytical forms for spherical and quadrupole form factors calculated deuteron tensor polarization t_2i. The result t_20(p) in wide area of momentas for NijmI, NijmII, Nijm93, Reid93 and Argonne v18 potentials agreed well with the literature results for other potential nucleon-nucleon models, and with experimental data of world collaborations (Bates, BLAST, JLab, NIKHEF, VEPP-3, Saclay) and reviews (Boden, Garcon, Abbott). Reduced quantity tensor polarization t_20R it is compared to experimental data. The obtained results will allow studying the deuteron electromagnetic structure, its form-factors, differential cross section of double scattering in more detail in future, and also for calculations the theoretical values of spin observables in dp-scattering.