Acoustic radiation force (ARF) is commonly used in ultrasound (US)-based elastography to generate shear waves deep within soft tissue. These waves can be detected with different methods, e.g. contact conventional ultrasound imaging probes or contact free magnetic resonance or optical coherence tomography (OCT). For many clinical applications, however, for instance the eye, a totally non-contact system for generation/detection of mechanical waves is needed. Here, we present a method for efficient non-contact excitation of broadband transverse mechanical waves in soft media. The approach is based on pushing the medium under study with a 1 MHz chirped US wave focused to its surface from air. The US beam reflected from the air/medium interface provides the ARF force to the medium surface launching a transient mechanical wave in the transverse (lateral) direction. The design and performance of the air-coupled transducer is discussed. The focal zone, peak pressure and acoustic intensity are measured for transducers with different numerical apertures. Time and frequency characteristics of the propagating mechanical waves, generated in soft tissue, are tracked with a phase-sensitive ultra-fast frame rate OCT imaging system. Application of the proposed method for non-contact, non-invasive, sub-mm resolution elasticity measurement in soft tissue is proposed.