We report theoretical investigations of the lattice dynamics of KCuF(3). Our calculations are based on the generalized gradient approximation and parametrization of Perdew-Burke-Ernzerhof to the density functional theory corrected for on-site Coulomb interaction (GGA + U). Vibrations of the KCuF(3) lattice are studied within the harmonic approximation. Energetic stability of tetragonal and orthorhombic polymorphic structures of KCuF(3) is analyzed. Our results show that the orthorhombic polymorph is energetically not preferred. The Raman and infrared-active phonon modes in two distinct tetragonal polymorphs of KCuF(3) are discussed with respect to the available experimental data. A detailed examination of the phonon densities of states in both tetragonal polymorphic structures of KCuF(3) is provided together with discussion on similarities and differences between the vibrational dynamics of two distinct tetragonal lattices of the KCuF(3) system.