In this study, 3D simulations based on a theoretical model were developed to investigate radiationinduced nanostructure formation in amorphous materials. Model variables include vacancy production and recombination rates, ion sputtering effects, and redeposition of sputtered atoms. In addition, a phase field model was developed to predict vacancy diffusion as a function of free energies of mixing and interfacial energies. The distribution profile of the vacancy production rate along the depth of an irradiated matrix was considered as a near Gaussian approximation according to Monte-Carlo TRIM code calculations. Dynamic processes responsible for nanostructure evolution were simulated by updating the vacancy concentration profile over time. Simulated morphologies include cellular nanoholes, nanowalls, nanovoids, and nanofibers, with the resultant morphology dependant upon the incident ion species and ion fluence. These simulated morphologies are consistent with experimental observations achieved under comparable experimental conditions. Our model provides a distinct numerical approach to accurately predicting morphological results for ion-irradiation-induced nanostructures.