A gas compressor, comprising: a compressor body; and a housing which covers the compressor body, the compressor body, including: a rotor which has an approximately cylindrical shape, and rotates around a shaft; a cylinder which has an inner circumferential surface having an outline shape surrounding the rotor from an outside of an outer circumferential surface of the rotor, and in which a discharge part is formed; a plurality of plate-like vanes which are provided to receive a back pressure from vane grooves formed in the rotor and freely protrude outward from the rotor; and two side blocks (20, 30) which are provided on both end surface sides of the rotor and the cylinder, wherein the compressor body is formed such that a plurality of compression chambers divided by the rotor, the cylinder, the side blocks (20, 30) and the vanes are formed inside, and each compression chamber performs only one cycle of intake, compression and discharge through the discharge part of gas in a period of one rotation of the rotor, and an outline shape of a cross-section of the inner circumferential surface of the cylinder is formed such that in the period of the one rotation of the rotor, the following regions 1 to 4 are consecutively provided in order of the regions 1 to 4: 1: a region in which a capacity of one of the compression chambers rapidly increases 2: a region in which the capacity of the one compression chamber rapidly reduces 3: a region in which a capacity reduction rate of the one compression chamber becomes smaller than a capacity reduction rate of the region 2 4: a region in which the capacity reduction rate of the one compression chamber becomes larger than a capacity reduction rate of the region 3, characterised in that a distant portion at which the inner circumferential surface of the cylinder and the outer circumferential surface of the rotor are most distant from each other in the inner circumferential surface of the cylinder is placed in a rotation angle range (β) which is located relatively below in a rotation angle range which is interposed between two rotation angle positions (αI, α2) where a posture of one of the vanes is in a horizontal state during the period of the one rotation of the rotor, and in that a protrusion amount of the vanes from the rotor is largest at the distant portion. a compressor body; and a housing which covers the compressor body, a rotor which has an approximately cylindrical shape, and rotates around a shaft; a cylinder which has an inner circumferential surface having an outline shape surrounding the rotor from an outside of an outer circumferential surface of the rotor, and in which a discharge part is formed; a plurality of plate-like vanes which are provided to receive a back pressure from vane grooves formed in the rotor and freely protrude outward from the rotor; and two side blocks (20, 30) which are provided on both end surface sides of the rotor and the cylinder, 1: a region in which a capacity of one of the compression chambers rapidly increases 2: a region in which the capacity of the one compression chamber rapidly reduces 3: a region in which a capacity reduction rate of the one compression chamber becomes smaller than a capacity reduction rate of the region 2 4: a region in which the capacity reduction rate of the one compression chamber becomes larger than a capacity reduction rate of the region 3,