The internal-meshing rotary compressor can be applied to the CO₂ transcritical refrigeration cycle due to its simple structure, self-balanced initial mass, and high pressure endurance. Because of the different fluids transmitted by compressor and pump, the design method of the internal meshing rotary pump cannot be entirely and directly employed. In order to simplify the further study of the internal-meshing rotary compressors, the essential profile equations for the inner and outer rotors are derived and explicitly formulated based on the equidistant curve of curtate epicycloid and the multi-section circular arc, respectively. Then, the relationship between the meshes of the inner and outer rotors, the position of the instantaneous center, the meshing range of the tooth tip arc, and the modification of the profiles are discussed. These basic geometric theories are expected to lay the principles for the design of the compressor of interest.