Head and neck posture is an important factor in neck pain related to computer use; however, the evidence for an optimal posture is unconvincing. This study measured the 3-D postures of 36 young adults during use of three different display heights. Cervical extensor muscle strain was estimated using modelled gravitational load moments and muscle capacities. The influence of more or less upper vs. lower cervical movement was also explored across a broad range of potential postures. Overall cervical extensor muscle capacity diminished away from a neutral posture whilst gravity moment increased with flexion. Overall cervical extensor muscle strain increased with head flexion but remained stable into head extension. Individual differences in the amount of upper and lower cervical movement had an important effect on strain, particularly for some muscles. Computer display height guidelines are an important component of ergonomics practice, yet the relative strain on neck extensor muscles as a function of display height has not been examined. The current findings provide more detailed biomechanical evidence that ergonomists can incorporate with usability and other evidence to determine appropriate display height recommendations.