The slumping and subsequent arrest of initially motionless granular materials from behind a rapidly removed lockgate in a sloping two-dimensional channel is considered theoretically and experimentally. The theory is based upon a shallow layer description of the flow and arrest of the grains in which resistance to the downslope motion is modelled as a Coulomb drag with a constant coefficient of friction. The flows leave a thin layer of deposited material along the chute and the depth of the deposit at the rear of the lock is predicted from the theoretical model using asymptotic techniques. This analysis explains the dependence on the initial aspect ratio of the release that has been seen in previous numerical and experimental studies of granular slumps over horizontal surfaces. The theoretical predictions of this depth are also compared with laboratory observations of the slumping of four dry granular materials. It is shown that there is quantitative agreement between the experimental measurements and the theoretical predictions, which include no fitting parameters. The theoretical predictions for the length along the chute that the materials slump, however, are not in agreement with the theoretical model and potential reasons for this mismatch are discussed.