Conditions are investigated under which a body lying at rest or rocking on a solid horizontal surface can be removed from the surface by hydrodynamic forces or instead continues rocking. The investigation is motivated by recent observations on Martian dust movement as well as other small-and large-scale applications. The nonlinear theory of fluid-body interaction here has unsteady motion of an inviscid fluid interacting with a moving thin body. Various shapes of body are addressed together with a range of initial conditions. The relevant parameter space is found to be subtle as evolution and shape play substantial roles coupled with scaled mass and gravity effects. Lift-off of the body from the surface generally cannot occur without fluid flow but it can occur either immediately or within a finite time once the fluid flow starts up: parameters for this are found and comparisons are made with Martian observations.