When a steadily moving load is applied to a floating ice plate, the disturbance will generally approach a steady state (relative to the load) as time t → ∞. However, for certain ‘critical’ load speeds the disturbance may grow continuously with time, which represents some danger to vehicles driving on ice. To understand this phenomenon and the overall time development of the ice response, this paper analyses the problem of an impulsively applied, concentrated line load on a perfectly elastic homogeneous floating ice plate. An exact expression for the ice deflection is derived, and then interpreted by means of asymptotic expansions for large t in the vicinity of the source. The spatial development of the disturbance is analysed by considering asymptotic expansions as t → ∞ near an observer moving away from the load. Theoretical results are compared with field measurements, and some hitherto unexplained features can be understood.