Orthorhombic α − MoO 3 is a layered oxide with various applications and with excellent potential to be exfoliated as a 2D ultra-thin film or monolayer. In this paper, we present a first-principles computational study of its vibrational properties. Our focus is on the zone center modes, which can be measured by a combination of infrared and Raman spectroscopy. The polarization dependent spectra are simulated. Calculations are also performed for a monolayer form in which "double layers" of Mo 2 O 6, which are weakly van der Waals bonded in the α -structure, are isolated. Shifts in phonon frequencies are analyzed.