A linear compressor comprising: a shell having a cylindrical shape with both ends open to form an inner space; a first shell cover and a second shell cover covering respectively a first end and a second end of the shell; a compressor body disposed in the shell to compress refrigerant; and a support device configured to connect the compressor body to the first shell cover to prevent the compressor body from contacting an inner peripheral surface of the shell; wherein the support device includes: a support spring formed with a hole in a central portion and having a spiral spring arm extending from the central portion to an outer portion, at least a portion of the outer portion being connected to the compressor body; wherein a cover support portion is formed on an inner surface of the first shell cover, a rigid connection portion spaced apart from the support spring in an axial direction by a predetermined distance; and an elastic connection portion formed to surround at least a portion of a periphery of the hole of the support spring to connect the support spring and the rigid connection portion and coupled to the first shell cover, the elastic connection portion being made of an elastic material, wherein an elastic protrusion of the elastic connection portion is inserted into the cover support portion to connect the support device and the first shell cover, and the rigid connection portion is received in the elastic connection portion so as to limit the elastic deformation range of the elastic connection portion, characterized in that the rigid connection portion is received in the elastic connection portion such that the rigid connection portion is spaced apart from the cover support portion to prevent direct contact between the rigid connection portion and the cover support portion. a shell having a cylindrical shape with both ends open to form an inner space; a first shell cover and a second shell cover covering respectively a first end and a second end of the shell; a compressor body disposed in the shell to compress refrigerant; and a support device configured to connect the compressor body to the first shell cover to prevent the compressor body from contacting an inner peripheral surface of the shell; wherein the support device includes: a support spring formed with a hole in a central portion and having a spiral spring arm extending from the central portion to an outer portion, at least a portion of the outer portion being connected to the compressor body; wherein a cover support portion is formed on an inner surface of the first shell cover, a rigid connection portion spaced apart from the support spring in an axial direction by a predetermined distance; and an elastic connection portion formed to surround at least a portion of a periphery of the hole of the support spring to connect the support spring and the rigid connection portion and coupled to the first shell cover, the elastic connection portion being made of an elastic material, wherein an elastic protrusion of the elastic connection portion is inserted into the cover support portion to connect the support device and the first shell cover, and the rigid connection portion is received in the elastic connection portion so as to limit the elastic deformation range of the elastic connection portion, characterized in that the rigid connection portion is received in the elastic connection portion such that the rigid connection portion is spaced apart from the cover support portion to prevent direct contact between the rigid connection portion and the cover support portion. a support spring formed with a hole in a central portion and having a spiral spring arm extending from the central portion to an outer portion, at least a portion of the outer portion being connected to the compressor body; wherein a cover support portion is formed on an inner surface of the first shell cover, a rigid connection portion spaced apart from the support spring in an axial direction by a predetermined distance; and an elastic connection portion formed to surround at least a portion of a periphery of the hole of the support spring to connect the support spring and the rigid connection portion and coupled to the first shell cover, the elastic connection portion being made of an elastic material, wherein an elastic protrusion of the elastic connection portion is inserted into the cover support portion to connect the support device and the first shell cover, and the rigid connection portion is received in the elastic connection portion so as to limit the elastic deformation range of the elastic connection portion, characterized in that the rigid connection portion is received in the elastic connection portion such that the rigid connection portion is spaced apart from the cover support portion to prevent direct contact between the rigid connection portion and the cover support portion.