An overlooked aspect of continental shelf wave generation by wind is that a non-wavelike flow field may accompany the waves. To explore this possibility, we calculate the response of an inclined plane shelf to suddenly applied alongshore wind, affecting a finite portion of the coast. The calculations are based on the classical theory of continental shelf waves, supposing low frequency motions and invoking the boundary layer approximation (alongshore scales much longer than cross-shore ones). The results reveal non-wavelike circulations, with or without bottom friction, on a shelf of finite or unlimited width, unaffected by changing offshore boundary conditions. In the frictionless case, the principal new feature is an accelerating coastal jet that feeds offshore Ekman transport, drawing the fluid from the outer shelf of the downwave half-space. Continental shelf waves accompany the coastal jet on a shelf of finite width, their properties varying with the shelf-edge boundary condition. With bottom friction, the non-wavelike circulation has the character of an "arrested topographic wave," a steady-state flow that develops on a gradually expanding portion of the inner shelf. This takes over the role of the coastal jet in the frictionless solution and satisfies mass balance by feeding offshore or onshore Ekman transport. The outer shelf is occupied by time-dependent closed circulations.