Vibrational spectra of BH4- and its isotopic analogues in a crystalline environment of alkali metals cations (K+, Rb+, Cs+) have been investigated beyond the harmonic approximation using a variational approach supported by computations of B3LYP type anharmonic force fields. From the comparison of the observed and simulated IR spectra, the influence of the anharmonic couplings on the band position and on the relative intensity of the allowed vibrational transitions is discussed. Here, the effect of the crystalline environment induces a blue shift of about 50 and 100 cm-1 respectively for the bending and stretching modes of BH4-. Furthermore, anharmonic effects, which are exclusively well reproduced by a variational approach, are needed to yield reliable positions and relative amplitudes of IR allowed combination and overtone transitions. This leads to theoretical results fitting their experimental counterpart between 6 and 30 cm-1 in the investigated series.