Compressor maps are one of the main elements describing the behaviour of centrifugal compressors. Although the compressor map is often provided by the manufacturer, there may be changes during the lifetime of the compressor due to refurbishments or wear. Since the compressor maps are often used in real-time optimization problems, there is a need for simple approximation methods. This paper focuses on approximation of physical models using Chebyshev polynomials instead of third order polynomials which are unable to capture some aspects of the compressor behaviour. Chebyshev polynomials capture the characteristics better than third order polynomials. They provide a flexible tool for compressor map approximation and analysis.