Methods and apparatus for producing synchronously pumped (SP) ultrasonic bursts which can be used to create ultrasound radiation pressure. The emission of an ultrasonic burst by a piezoelement is synchronized with the reflection of another ultrasonic burst by the same piezoelement to create a combined ultrasonic burst with increased amplitude. Repeated synchronized emissions and reflections of ultrasonic bursts lead to resonant growth of a burst amplitude to equal that of a standing wave, but without formation of a nodal structure. In some embodiments, the SP ultrasonic bursts generate shear waves. In some embodiments, the shear waves are resonant shear waves. In some embodiments, the shear waves are formed in a supersonic regime. Shear waves thus formed can be used for various treatments of biological tissues, with or without RF heating.