Abstract: An anaerobic reactor comprising two or more discrete reaction chambers arranged one above the other is disclosed. The reactor may be in the form of a tank separated into discrete chambers by means of solid members, or the reactor may be in the form of separate and stackable chambers. Additionally, the reactor may be a packed bed reactor, a fluidised bed reactor, or a hybrid reactor comprising at least one packed bed reaction chamber and at least one fluidised bed reaction chamber. Use of an anaerobic reactor according to the invention enables an increase in the yield of biogas that can be produced per unit area of land occupied by an anaerobic reactor. A method of producing biogas is also disclosed, the method comprising providing an anaerobic reactor according to the invention, providing input biomass, carrying out anaerobic digestion of the biomass in the reactor, and collecting the biogas produced.