Intramolecular tunneling of a hydrogen atom in formic acid at low temperatures has been studied theoretically on the basis of quantum-chemical modeling of HCOOH@Nb(12) clusters. Three noble matrixes (Ar, Kr, and Xe) are considered. Energetic and geometric parameters as well as vibrational frequencies for the formic acid in cis and trans configurations surrounded by 12 Nb atoms are calculated within the frame of the MP2 approach with extended basis sets. The rate constant of HCOOH cis-trans conversion is analyzed by taking into account matrix reorganization and the change of HCOOH position in the cluster. The matrix reorganization is considered within the Debye model of lattice vibrations, whereas the external motion of HCOOH in the cluster is treated using the Einstein model of solids. It has been shown that the literature experimental data on the cis to trans tunneling reaction in the formic acid can be accounted for within the proposed mechanism, which describes the matrix reorganization and the change of the HCOOH position in the noble gas matrix, with fitting parameters of the suggested theoretical model attaining reasonable values.