A multi-stage anaerobic digester is designed to treat a high solids, stackable feedstock. The system may also receive a pumpable feedstock such as a slurry or sludge. In a first stage, the digestate circulates in one direction around a raceway such that the digestate may pass a feed inlet multiple times before leaving the first tank. An optional side stream loop withdraws fibrous material from near the top of the reaceway and return digestate with chopped fibers, preferably lower and further along the raceway. An outlet from the raceway located near, but upstream of the feed inlet discharges partially digested substrate to a second stage, which is operated as a stirred tank reactor. The two stages may be provided in a single tank with an internal wall separating a ring shaped outer portion from a cylindrical inner portion. The digester may be operated in a thermophilic temperature range.