Methods for steady state operation of an upflow anaerobic digester using organic matter that contains a portion of solid, non-digestible matter include (1) providing an upflow anaerobic digester, (2) providing a bacterial culture in the upflow anaerobic digester for the breakdown of organic matter, (3) introducing an influent into the upflow anaerobic digester, wherein the influent comprises a biodegradable component, a liquid component, and an amount of solid non-digestible matter, (4) operating the upflow anaerobic digester in a steady-state, (5) accumulating the solid, non-digestible matter in the upflow anaerobic digester, (6) and removing a portion of the accumulated solid, non-digestible matter from the upflow anaerobic digester through the bottom of the upflow anaerobic digester while maintaining steady-state operation of the upflow anaerobic digester. Steady-state operation of the upflow anaerobic digester is maintained by selecting a percentage of the total volume of the liquid and material that are flushed from the digester for a given period of time so as to preserve the steady-state of the bacterial culture.