To develop a minimal model for a cell moving in a crowded environment such as in tissue, we investigate the response of a liquid drop of active matter moving on a flat rigid substrate to forces applied at its boundaries. Our model incorporates active stresses due to a prescribed orientation profile of the cytoskeleton, coupling with the substrate, surface tension and imposed boundary forces. We find a highly non-linear response to forces that we characterise using the drop velocity, its shape, and the traction between the drop and the substrate. There are two main modes of motion: a long and thin drop with zero traction in the bulk, mostly occurring under strong stretching forces, and a parabolic drop with finite traction in the bulk, mostly occurring under strong squeezing forces. There is a sharp transition between these two modes as a function of the applied forces and indications of drop break-up where large forces stretch the drop in opposite directions.
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