Healthy elderly people walk slower and energetically less efficiently than young adults. This decline in walking performance lowers the quality of life for a growing ageing population, and understanding its physiological origin is critical for devising interventions that can delay or revert it. However, the origin of the decline in walking performance remains unknown, as ageing produces a range of physiological changes whose individual effects on gait are difficult to separate in experiments with human subjects. Here we use a predictive neuromechanical model to separately address the effects of common age-related changes to the skeletal, muscular and nervous systems. We find in computer simulations of this model that the combined changes produce gait consistent with elderly walking and that mainly the loss of muscle strength and mass reduces energy efficiency. In addition, we find that the slower preferred walking speed of elderly people emerges in the simulations when adapting to muscle fatigue, again mainly caused by muscle-related changes. The results suggest that a focus on recovering these muscular changes may be the only effective way to improve performance in elderly walking.