Cyclic finite element simulations of complex materials, for example, polycrystalline metals, are widely used to study fatigue failure due to plasticity and damage. Typically, this requires the simulation of a large number of cycles to failure for accurate determination of evolving deformation variables. Modeling cyclic deformation using conventional methods of time integration in semidiscretization techniques can however be computationally challenging. Single time scale integration methods typically follow the high frequency characteristics and discretize each cycle into a number of time steps over which integration is performed. To overcome this computational challenge, the wavelet transformation-based multitime scale (WATMUS) method proposed in an earlier work by the authors is advanced and validated in this paper to perform accelerated finite element simulations of materials undergoing rate-dependent plasticity for large number of cycles. Specifically, the WATMUS algorithm is integrated with crystal plasticity finite element method to perform accelerated simulations of polycrystalline alloys. The WATMUS methodology is also endowed with adaptive capabilities to optimally construct the wavelet basis functions and determine coarse-scale cycle steps. Accuracy and efficiency of the WATMUS methodology is conclusively demonstrated by comparing the results with cyclic single-time scale crystal plasticity finite element simulations performed on image-based microstructure of titanium alloys. Copyright © 2012 John Wiley & Sons, Ltd.