The subject invention provides advantageous systems and processes for anaerobic digestion of organic waste streams, particularly agricultural waste streams. According to this invention, a new process is provided in which a liquid fraction from an organic waste stream comprising soluble compounds is segregated and incubated in a reactor separate from the solids fraction of the organic waste stream. Digestion of waste in both reactors occurs substantially simultaneously and both reactors produce biogas (thus both reactors function essentially like single stage reactors but allow for continuous or intermittent loading). According to one aspect of the invention, at least one cross-flow baffle is provided for use in an anaerobic digester to collect biogas and break up clumped solids in the reactor. In another aspect of the invention, packing media for use in an anaerobic digester is provided.