Flexible electronics are a very promising technology for various applications. Several types of flexible devices have been developed, but there has been limited research on flexible electromechanical systems (MEMS). Surface acoustic wave (SAW) devices are not only an essential electronic device, but also are the building blocks for sensors and MEMS. Here we report a method of making flexible SAW devices using ZnO nanocrystals deposited on a cheap and bendable plastic film. The flexible SAW devices exhibit two wave modes - the Rayleigh and Lamb waves with resonant frequencies of 198.1 MHz and 447.0 MHz respectively, and signal amplitudes of 18 dB. The flexible devices have a high temperature coefficient of frequency, and are thus useful as sensitive temperature sensors. Moreover, strong acoustic streaming with a velocity of 3.4 cm/s and particle concentration using the SAW have been achieved, demonstrating the great potential for applications in electronics and MEMS.