Platinum aluminides have the prospect of being used as both functional and structural materials for a range of scientific and technical tasks. They possess unique properties that make them effective catalysts. The dynamics of the crystal lattice play an important role in the manifestation of these properties. In this study, an analysis of the density of phonon states of crystals and the possibility of the existence of localized lattice vibrations in Al and Pt alloys is conducted using atomistic modeling. The following compounds are considered: AlPt, Al2Pt, Al3Pt, AlPt2, Al3Pt5, AlPt3 (four types of lattices). The calculated phonon spectra allow for the assessment of the possibility of the existence of nonlinear localized modes in the forbidden zone of the spectrum, if it is present. It is shown that a number of crystals within the framework of the considered formalism and interatomic potential can have a forbidden zone. This condition, together with the nonlinearity of the bonds, ensures the existence of highly-amplitude localized modes in the following compounds: AlPt3, AlPt3(1), AlPt3(2), AlPt3(3). It is also established that in the Al3Pt5 alloy, the existence of prolonged high-amplitude excitations on the Al atom is possible.