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To study the connection between macroscopic hysteretic behavior and the microstructural properties, this paper presents and validates a new material dependent three-dimensional mesoscopic magnetic hysteresis model. In the presented mesoscopic description, the different micromagnetic energy terms are reformulated on the space scale of the magnetic domains. The sample is discretized in cubic cells, each with a local stress state, local bcc crystallographic axes, etc. The magnetization is assumed to align with one of the three crystallographic axes, in positive or negative sense, defining six volume fractions within each cell. The micromagnetic Gibbs free energy is described in terms of these volume fractions. Hysteresis loops are computed by minimizing the mesoscopic Gibbs free energy using a modified gradient search for a sequence of external applied fields. To validate the mesohysteresis model, we studied the magnetic memory properties. Numerical experiments reveal that (1) minor hysteresis loops are indeed closed and (2) the closed minor loops are erased from the memory.