Various classifications of fuel accumulation models are used to describe the complex temporal relationship between fuel loads and vegetation dynamics. Fuel accumulation models are an important tool in wildfire management as fuel is the only component that can be directly controlled by fire managers. Here we discuss various strengths and limitations of analytical fuel accumulation models that exist in the literature, with a focus on those used in Australia. Early approaches to analytical or continuous models of fuel accumulation centred around the model introduced by Olson in 1963. This model assumes that the rate at which fuel accumulates is determined as a balance between the rate of fuel accession and the rate at which it decays. The Olson model has been shown to provide a reasonable description of litter accumulation, data sparsity issues notwithstanding, but can be of limited use in describing elevated fuels, or in forest stands that exhibit more complex post-disturbance dynamics. Interactions between species and other disturbances have the potential to change the dynamics of fuel accumulation and decay processes. Moreover, post-fire vegetation stands are usually dominated by an understorey layer that eventually senesces as the dominant vegetation grows. Motivated by the critical differences between the models presented, a more general approach featuring vegetation density is proposed. A generic result is presented to indicate how the theoretical predictions of the model are able to emulate patterns of fuel accumulation that have been reported, and that can not be accounted for by the models commonly used in Australia.