Micro power generators (MPGs) can harvest electrical power from ambient energy resources in natural environments to operate small-scale electronic devices. Such systems exploit structural vibrations due to cross-flow instabilities through fluid–structure interactions (FSI). Due to attractive features of piezoelectric transducers, we utilize them for vibration-to-electricity conversion in this work. We develop strongly coupled FSI-based computational models to handle large-amplitude structural motions in which unsteady forces exerted by fluid flows on structures, their dynamical responses, and harvested power are directly computed. Our mathematical model for incompressible flows over moving bodies relies on arbitrary Lagrangian–Eulerian (ALE) formulation. Our in-house FSI solver primarily works using radial basis interpolation technique for grid morphing. Using broad ranges of fluidic, structural, and electrical parameters, we investigate the power generation performance of two types of MPGs, working through vortex-induced vibrations of a circular cylinder and a fluttering NACA-0012 airfoil, under different excitation conditions. Optimum values of load resistance are found to maximize the harvested power. Furthermore, our findings support the linear analysis, which provides insights into the possible instabilities in the electro-mechanical system. Another salient feature of this research work is the inclusion of cubic nonlinear stiffness in the energy harvesting models. [ABSTRACT FROM AUTHOR]