The polarized Raman spectra of the Cu₂ZnSiS₄ and Cu₂ZnSiSe₄ single crystals were investigated as a function of the in-plane rotation angle on the basal (210) crystal planes. The position of up to 32 (for the sulphide compound) and 27 (for the selenide compound) Raman peaks was determined for each of the compounds in the spectral region 50-600 cm^-1. A careful analysis of the high resolution spectra that were measured under different polarization configurations has allowed determining the A₁(TO), A₂, and B₁/B₂(TO + LO) symmetry of the dominant and some weaker Raman modes. The investigation of the dependence of the intensity of the peaks with the rotation angle has corroborated the symmetry assignment of the main modes and has allowed to estimate numerical values of Raman tensor elements for these compounds. The importance of anharmonic one-two phonons interaction in the Raman spectra of the investigated crystals is discussed.