Auditory nerve fibres (ANFs) are classified into low, medium and high spontaneous rates (SRs). Hearing impairments caused by the loss of these different types of ANF are difficult to differentiate. We estimated the impact of different types of ANF loss on processing of amplitude modulation (AM). A physiologically inspired computational model and hearing loss simulator, MAPsim, was used to simulate the impact of different types of ANF loss on the encoding and perception of AM signals. All modelled ANFs shifted their dynamic range to adapt to the prevailing sound level, but the low- or medium-SR ANFs showed much better phase locking to AM than high-SR fibres. Furthermore, psychophysical measures and computational modelling of AM perception showed that removing high-SR fibers had little impact on supra-threshold AM perception, but removing low-SR fibers significantly degraded performance on tasks that rely on AM cues; AM detection and understanding of unvoiced speech in noise were only degraded by loss of low-SR fibres. However, natural speech in noise, which provides fine-structure information, showed smaller deficits from the loss of low-SR fibres. The study illustrates the potential of using AM-based tasks as a differential diagnostic tool for different types of auditory nerve damage.