The interaction between phonons and photons is investigated theoretically in a phoxonic cavity inside a corrugated nanobeam waveguide presenting band gaps for both electromagnetic and elastic waves. The structure is made by drilling periodic holes on a silicon nanobeam with lateral periodic stubs and the tapered cavity is constructed by changing gradually the geometrical parameters of both the holes and stubs. We show that this kind of cavity displays localized phonons and photons inside the gaps, which can enhance their interaction and also promotes the presence of many optical confined modes with high quality factor. Using the finite-element method, we demonstrate that with appropriate design of the tapering construction, one can control the cavity modes frequency without altering significantly the quality factor of the photonic modes. By changing the tapering rates over the lattice constants, we establish the possibility of shifting the phononic cavity modes frequency to place them inside the desired gap, which enhances their confinement and increases the mechanical quality factor while keeping the strength of the optomechanic coupling high. In our calculations, we take account of both mechanisms that contribute to the acousto-optic interaction, namely photoelastic and interface motion effects. We show that in our case, these two effects can contribute additively to give high coupling strength between phononic and photonic cavity modes. The calculations of the coupling coefficient which gives the phonon-photon coupling strength give values as high as 2 MHz while photonic cavity modes display quality factor of 105 and even values up to 3.4 MHz but with smaller photonic quality factors. ; Oudich, M.; El-Jalla, S.; Pennec, Y.; Djafari-Rouhani, B.; Gomis Bresco, J.; Navarro-Urrios, D.; Martínez Abietar, AJ. (2014). Optomechanic interaction in a corrugated phoxonic nanobeam cavity. Physical Review B. 89:245122-245130. doi:10.1103/PhysRevB.89.245122. ; Senia ; 245122 ; 245130 ; 89