The invention relates to a process for anaerobic treatment of material having a solids concentration greater than 15% in a digester in the form of a sealed tank (1) equipped with means (2) for supplying material to be treated and means (3) for discharging digested material and also vertical homogenization means (6) in the form of injectors for injecting a gaseous fluid into the bottom (7) of the tank (1). Through distribution in the tank (1) of the material supply means (2) relative to the discharge means (3) and using vertical homogenization means (6) that guarantee the homogeneity of the material treated by vertical sectors (8) in the tank, conferred on the material in the tank (1) is a forced unidirectional circulation that is uniform throughout the entire cross section of this tank, and along one substantially horizontal component, between said supply means (2) and said discharge means (3). The invention also relates to an installation for implementing such a process.