Cyclic deformation experiments have been performed on three titanium alloy microstructures to facilitate calibration of two distinct simplified polycrystal plasticity model frameworks. These microstructures include Ti–6Al–4V β-annealed, Ti-18 in a solution-treated, age-hardened (STA) condition (Fanning, 2011), and Ti-18 with a beta-annealed, slow-cooled, age-hardened (BASCA) treatment. Experimental results suggest that superior uniaxial yield strength, ultimate strength and tensile ductility are achieved through the STA processing for the Ti-18 material. This processing route produces a fine bi-modal microstructure. In contrast, corresponding measured properties of the Widmanstätten morphology generated via the BASCA heat treatment were lower. The constitutive frameworks for the two different simplified polycrystal plasticity models and associated flow rules have been outlined and the model parameters have been estimated for cyclic loading such that the simulated stress–strain response is consistent with experimental results for each of the titanium microstructures investigated. In view of envisioned application to fatigue, focus is placed on cyclic behavior after the initial loading cycle(s). Certain estimated parameters differ for each model among microstructures, mainly related to elasticity, threshold for slip system yielding, and work hardening; this suggests limits on a simplified model framework and the need for in situ studies of dislocation-interface reactions and the relative role of β-phase fraction. •Cyclic deformation experiments were performed on three Ti alloy microstructures.•Two crystal plasticity models were outlined and calibrated to experimental results.•Simulated polycrystals were fit to structure statistics acquired from EBSD analysis.•The calibrated simulation results are found to closely agree with experimental data.