Reciprocal movement cannot be used for locomotion at low-Reynolds number in an infinite fluid or near a rigid surface. Here we show that this limitation is relaxed for a body performing reciprocal motions near a deformable interface. Using physical arguments and scaling relationships, we show that the nonlinearities arising from reciprocal flow-induced interfacial deformation rectify the periodic motion of the swimmer, leading to locomotion. Such a strategy can be used to move toward, away from, and parallel to any deformable interface as long as the length scales involved are smaller than intrinsic scales, which we identify. A macro-scale experiment of flapping motion near a free surface illustrates this new result.Swimming microorganisms inhabit a world quite different from the one we experience. Their motion through the surrounding fluid occurs at very low Reynolds numbers (Re), a fact with two important consequences: (a) the only physical force available to produce thrust is drag; (b) since the fluid equations (Stokes equations) are linear and time-reversible, swimming motions symmetric with respect to time reversal (reciprocal motion) cannot be used for locomotion (the scallop theorem [1]). Biological swimmers, such as bacteria and spermatozoa, overcome these two limitations by exploiting the anisotropic drag of slender filaments such as flagella and cilia, and actuating these filaments in a wave-like fashion [2,3].Motivated by the recent development of artificial swimmers [4], we pose here the following general question: are there any new low-Re swimming methods remaining to be discovered? In particular, can some simple reciprocal movements produce locomotion, thereby apparently violating the constraints of the scallop theorem?In this paper, we propose a new method for locomotion without inertia. Using theory and experiments, we show that a body performing a reciprocal movement is able to move near a soft interface: physically, the deformation of the interface provides the geometric nonlinearities necessary to escape the constraints of the scallop theorem. This strategy, which is relevant for sufficiently small systems, also implies that the time-reversible component of all swimmers (including biological organisms) can generate non-trivial flows and propulsive forces near soft interfaces.The physical picture for soft swimming arises from the asymmetries between different modes of motion near deformable interfaces, and can be illustrated by considering the motion of a rigid sphere slowly translating below a free surface ( Fig.