A linear compressor having a cylinder (2) and a piston (1) that is moved by an electric linear motor (4, 5, 6) is provided with one or more elastic elements (30, 50) made of steel wire having a central volute portion (30a, 50a). A leg (30b, 30c, 50b, 50c) extends from each end of the central volute portion (30a, 50a). In a first embodiment, one of the legs (30b) is fastened internally of the piston (1) and the other leg (30c) to a part of the cylinder (2). In a second embodiment, the central volute portion (50a) is mounted directly to the piston (1) and the two legs (50b, 50c) are fixedly connected to the cylinder (2). When the piston is moved by the action of the electric linear motor, the wire of the central volute portion of the elastic element distorts and stretches in the direction of travel of the piston. It is preferred that several elastic elements be mounted to the piston (1) having like portions of the central volute portion angularly spaced apart. Such arrangement provides a more equal distribution of the forces of the piston acting against the central volute portions of the elastic elements.