The human visual system perceives 3D depth following sensing via its binocular optical system, a series of massively parallel processing units, and a feedback system that controls the mechanical dynamics of eye movements and the crystalline lens. The process of accommodation (focusing of the crystalline lens) and binocular vergence is controlled simultaneously and symbiotically via cross-coupled communication between the two critical depth computation modalities. The output responses of these two subsystems, which are induced by oculomotor control, are used in the computation of a clear and stable cyclopean 3D image from the input stimuli. These subsystems operate in smooth synchronicity when one is viewing the natural world; however, conflicting responses can occur when viewing stereoscopic 3D (S3D) content on fixed displays, causing physiological discomfort. If such occurrences could be predicted, then they might also be avoided (by modifying the acquisition process) or ameliorated (by changing the relative scene depth). Toward this end, we have developed a dynamic accommodation and vergence interaction (DAVI) model that successfully predicts visual discomfort on S3D images. The DAVI model is based on the phasic and reflex responses of the fast fusional vergence mechanism. Quantitative models of accommodation and vergence mismatches are used to conduct visual discomfort prediction. Other 3D perceptual elements are included in the proposed method, including sharpness limits imposed by the depth of focus and fusion limits implied by Panum's fusional area. The DAVI predictor is created by training a support vector machine on features derived from the proposed model and on recorded subjective assessment results. The experimental results are shown to produce accurate predictions of experienced visual discomfort.