Abstarct: We have studied the deformed triaxial atomic nuclei using Bohr model which describes the even-even quadrupole deformed nuclei. The solutions of the eigenvalue equation of the Bohr Hamiltonian with suitable potentials provide a consistent frxamework to describe the structure of the quadrupole deformed nuclei. The suitable potential functions describing the triaxial nuclei have been introduced. The Bohr Hamiltonian has been solved with suitable potentials to investigate the structure of the triaxial nuclei in the critical points in which shape phase transitions occur. The physical observables, energy spectra and electric quadrupole transition rates, have been obtained and are compared to the theoretical and empirical results of the other works. Shape phase transitions in triaxial nuclei have been investigated.