Compression-shear-induced tilt azimuthal orientation of amphiphilic monolayer in tilting phases (L2 and L'2) at the air-water interface is analyzed as dynamical equilibrium of the elastic distortion of orthogonally hexagonal structure of the molecules under compression-induced shear flow. It is shown theoretically that the compression can induce molecular tilts lying along and/or against the flow direction. All these tilts makeup the initial random tilt azimuth of the molecular tails along a uniform direction. At a threshold compression speed, it causes a C(infinity)-->C(2v)-symmetry transition at the air-water interface. With Maxwell displacement current and optical second-harmonic generation measurements, the above theoretical results are verified experimentally in a monolayer of 4-heptyloxy-4(')-cyanobiphenyl.