Orthostatic intolerance following spaceflight remains a critical problem in the current life-science space program. The study presented in this paper is part of an ongoing effort to use mathematical models to investigate the effects of gravitational stresses on the cardiovascular system of normals and microgravity adapted individuals. We employ a twelve compartment lumped parameter representation of the hemodynamic system coupled to set-point models of the arterial baroreflex and the cardiopulmonary reflex to investigate the transient response of heart rate to orthostatic stress. We simulate current hypotheses concerning the mechanisms underlying post-spaceflight orthostatic intolerance over a range of physiologically reasonable values and compare the simulations to astronaut stand-test data pre- and post-flight. Furthermore, we explore the effects of a potential countermeasure.