An exact solution is presented for the problem of unsteady natural convective radiating flow in an open-ended vertical channel. Laplace transform technique is used to obtain the analytical solutions for the velocity and temperature fields in the optically thin limit case when the channel walls temperature are maintained at different constant temperatures. The effects of radiation parameter and Grashof number on the flow fields are discussed through graphs. It is found that the effect of radiation is to decrease the fluid velocity whereas the effect of Grashof number is to increase the fluid velocity in the vertical channel. © 2013 AIP Publishing LLC.