In this paper we consider some unsteady free convection flows of a Bingham fluid when it saturates a porous medium. These flows are induced by suddenly raising the constant temperature of a vertical bounding surface from that of the uniform ambient value to a new constant level. As time progresses heat conducts inwards and this induces flow. We consider both a semi-infinite domain and a vertical channel of finite width. Of interest here are (i) how the presence of yield surfaces alters the classical results for Newtonian flows and (ii) the manner in which the locations of the yield surfaces change as time progresses. (C) 2014 Elsevier Ltd. All rights reserved.