The literature on solid-state digestion (SSD) reveals no convincing physical model of the process. Most of the reported reaction models implicitly assume homogeneity: the heterogeneous nature of the waste substrate may be noted but is rarely modelled. In contrast, this paper proposes an essential role for heterogeneity. A multi-zoned physical model and a localized reaction site are consistent with many characteristics of SSD. The fundamental hypothesis is that methanogenesis requires sites protected from the rapid acidogenesis occurring in the richer elements of the waste. If this protection is provided by mass-transfer resistances within pockets of leaner material, it is essential that their identity is not destroyed by excessive mixing or size reduction. A possible mechanism for such an effect is furnished by the proposed model, with a central role for mass transfer. Reaction is envisaged as occurring only in a thin layer, at an interface between rich and lean material. Acetogenesis and methanogenesis take place in distinct zones, with the latter protected from acid inhibition by mass-transfer resistances in an intervening buffer zone. The rate of waste stabilization is determined by the rate of advance of this multi-zoned reaction front. Several of the mass transfer processes occurring between these zones could be rate-limiting. This model suggests that methanogenesis in a typical landfill gradually spreads from discrete initiation points, with the reaction zones forming an expanding set of concentric shells. Process optimization may thus require maximizing the number of initiation points, subject to a constraint: only the larger seed fragments can develop. Reported failures to replicate the process at laboratory scale might thus be due to the use of homogenized feedstock. The implications of the model for commercial practice are discussed, as are potential methods of experimental verification.