Experimental measurements of the second order susceptibilities for the second harmonic generation are reported for YAl 3 (BO 3 ) 4 (YAB) single crystals for the two principal tensor components xyz and yyy. First principle's calculation of the linear and nonlinear optical susceptibilities for Yttrium Aluminum Borate YAl 3 (BO 3 ) 4 (YAB) crystal have been carried out within a framework of the full-potential linear augmented plane wave (FP-LAPW) method. Our calculations show a large anisotropy of the linear and nonlinear optical susceptibilities. The observed dependences of the second order susceptibilities for the static frequency limit and for the frequency may be a consequence of different contribution of electron-phonon interactions. The imaginary parts of the second order SHG susceptibility , , , and are evaluated. We find that the 2ω inter-band and intra-band contributions to the real and imaginary parts of show opposite signs. The calculated second order susceptibilities are in reasonable good agreement with the experimental measurements.