We report on the first observation of folded acoustic phonons in the Raman spectra of short-period AlN/GaN superlattices (SLs). The values of longitudinal and transverse sound velocities along the  direction of SL were estimated. It is shown that the SL period can be evaluated from Raman data with a good accuracy. Ab initio calculations of the zone-center phonons in (AlN)n(GaN)n SLs with the number of monolayer equal to n = 2,4,6 were performed. The frequencies of phonon modes were calculated and the mode displacement patterns have been established. The theoretical Raman spectra were simulated and compared with experimental ones. A strong sensitivity of A1(LO) phonons confined within the AlN layer to its thickness was revealed both experimentally and in calculations. This finding can be used for quantitative characterization of short-period AlN/GaN SLs.