Optical second harmonic generation in CsLiB6O10 (CLBO) large-sized nanocrystallites (15-40 nm) incorporated into the olygoether photopolymer matrices has been found at liquid helium temperature (LHeT). The second harmonic generation (SHG) has been measured for the source wavelength of the YAG : Nd laser (lambda = 1.06 mum). Increasing acoustical power (up to 18.1 W/cm(2)) and acoustical frequencies at 14 kHz give maximal values of the output SHG. The measured SHG chi (222) tensor component was comparable with the one for the traditional nonlinear optical crystals such as KH2PO4, KTiOPO4, LiNbO3. With decreasing temperature below 28 K the acoustically induced SHG signal strongly increases. A correlation between the acoustically induced SHG and low-frequency Raman modes has been found. The maximal acoustically induced SHG has been observed for the nanocrystallite concentration about 3.1% (in weighting units) and the crystallite sizes lying within the 35-40 nm. The SHG tensor coefficients were higher than for the proper CLBO crystals at least on the 13%. Advantageous and drawbacks of the presented model are discussed. The theory of the observed phenomena is explained on the ground of ab initio band energy calculations with taking into account of anharmonic electron-phonon interactions.