Using a mathematical tool for compressing audio recordings The research work consists of creating an algorithm for compressing an audio file with minimal loss of quality by splitting the graph of the intensity of the audio signal from time to time into parts bounded by extremes – one minimum and a maximum – and replacing each segment with an approximating cubic function found using the least squares method. The paper considered methods of digitization for FLAC and MP3 formats, highlighted their disadvantages and advantages, and also described in detail its own algorithm, which consists in replacing the data set (sample number and corresponding audio signal power at its interval) with a number of cubic functions, as well as the length during which each of them will be used. I had to face a number of problems, in particular, inaccuracy of the approximation method, irrationality of the interpolation method (low accuracy and poor compression ratio), the appearance of noise in the software implementation of the codec, and so on. The result of the study was an audio file compression algorithm with its software implementation. The prospect of further research is to simplify the compression algorithm, increase the efficiency of the model, and reduce discrepancies between the input data and the approximation function. All visual content is copyrighted. Key words: audio file, encoding, compression algorithm, signal, approximation.