The article deals with the proble of finish machining the internal surfaces of straight and curved pipe parts of rectangular cross-section. There is carried out analysis of technological capabilities of special finish machining technologies of internal surfaces in the Russian Federation. General information, disadvantages and advantages of these methods are presented. The selection criterion is the uniformity of machining on straight and curved parts of the pipe part. There are proved the main advantages of choosing an abrasive flow machining method as a fairly inexpensive method of finish machining. A scheme for finish machining the internal surfaces of rectangular parts is proposed. The composition of the working medium has been chosen, which allows for uniform machining, including in the corners of a rectangular cross-section.