Flexible acoustic wave devices (FAWDs) have been explored for various applications where bending is inevitable. However, theoretical investigations of bending behavior of FAWDs hitherto are mostly done in the linear deformation regime. Herein, we develop a multi-sublayer model based on a stiffness matrix method for analysis of frequency shifts of surface acoustic wave (SAW) and Lamb waves under elasto-plastic deformations. Using this model, we calculate the frequency shifts for the cases of both an elastic bending and an elasto-plastic bending. Experimental frequency shifts of ZnO/Al flexible devices show good agreements with the theoretical results in the elastic bending tests (with a relative error of strain sensitivity < 3%), and also show relatively good agreements with the qualitative theoretical predictions in the nonlinearly elasto plastic bending tests. For three successive bending and recovery processes, the experimentally obtained frequency shifts show good repeatability in the elastic and elasto-plastic bending stages, demonstrating maximum relative errors of strain sensitivities less than 6.1% and 18.2%.