In this study, the hyperbolic-sine type constitutive equation was used to model the flow stress of annealed AZ61 magnesium (Mg) alloys. Hot compression tests were conducted at the temperatures ranging from 250 1C to 450 1C and at the strain rates ranging from 1 ? 10-3 s ? 1 to 1 s ? 1 on a Gleeble-3500 thermo-simulation machine. Constitutive equations as a function of strain were established through a simple extension of the hyperbolic sine constitutive relation. The effects of annealing heat treatments on the variations in constitutive parameters with strain were discussed. The hot compressive flow curves exhibited typical features of dynamic recrystallization. Multiple peak flow curves were observed in the annealed specimens upon testing at a strain rate of 1 ? 10 ? 1 s-1 and at various temperatures. Variations in constitutive parameters with strain were related to flow behavior and dependent on the initial conditions of the test specimens. The flow stresses of annealed AZ61 Mg alloys were predicted well by the strain-dependent constitutive equations of the hyperbolic sine function under the deformation conditions employed in this study.