Zeolites are a group of microporous aluminosilicate frameworks with numerous applications in, for example, catalysis and ion-exchange and sorption processes. One of the most important tools for analyzing the properties of zeolite structures is vibrational spectroscopy. However, the complexity of these structures often leads to difficulties when attempting to interpret the resulting spectra, so an additional complementary tool is required: computational methods. The aim of this study was to formulate a simplified periodic model of an LTA framework containing alkali metal cations (either Li(+), Na(+), K(+), Rb(+), or Cs(+)) and to perform a set of ab initio calculations aimed at assessing the influence of these cations on the properties of the vibrational spectra of the LTA framework. Additionally, chemical bonding was analyzed by means of electron density topology analysis. Results obtained were compared with experimental spectra for alkali metal forms of zeolite A. It was found that the vibrational spectra obtained using the proposed model agree well with the corresponding experimentally derived spectra, meaning that the model can be used to analyze real spectra in detail.