Background and Objectives: This work is devoted to the study of the influence of moisture of alabaster (building plaster) samples on the profiles of their IR spectra in the wave number range of 500–4000 cm−1. Materials and Methods: IR spectra of distilled water and alabaster samples with the moisture of 0, 26, 106, 132, 159, 185 and 212% at 23°C were investigated by experimental methods of disturbed total internal reflection. Wave numbers and intensities of components of IR spectra of CaSO4(H2O)n clusters for 0<n<16 were calculated by the methods based on density functional theory with exchange-correlation potential XLYP. Using Gaussian curves with the widths estimated from experiment, the profiles of water valence oscillation bands were determined. When calculating the structure of CaSO4(H2O)n, the positions of atoms in various structural modifications of clusters were optimized. The minimum total energy served as a criterion for choosing the optimal cluster structure, and for the clusters with a large number of atoms, this criterion was applied to an initially selected isomer. Conclusion: On the basis of the calculation results the transformations of the measured spectra (changes of wave numbers and intensities) with changes in the moisture content of the samples have been explained. Comparison of experimental and theoretical spectra in the 3500–3900 cm−1 range allowed to attribute the investigated alabaster powder to a combination of clusters of different sizes:2(CaSO4(H2O)0.5), 2(CaSO4(H2O)0.5 + 0.5H), 4(CaSO4(H2O)0.5), including a cluster of crystalline gypsum: 2(CaSO4(H2O)2). The achieved agreement in the the positions and profiles of the experimental and theoretical water bands in the spectra of samples of different moisture justifies the adequacy of the theoretical description of hydration of CaSO4.