Slug flow is a very common occurrence in gas-liquid two-phase how. Usually, it is an unfavorable flow pattern due to its unsteady nature, intermittency and high-pressure drop. For the calculation of the pressure drop and void fraction the commonly used approach is to treat an average slug unit with the assumption that all slug units are identical. This approach may be adequate for many engineering calculations but it fails to predict the true nature of slug movement in a pipeline. In many cases the information as to the length distribution and, in particular, the maximum possible slug length is of major interest. Recent efforts, to address this; problem, are based on a calculation scheme that can follow each slug and predict its evolution, growth or decay, as it moves along the pipe. Some success was reported for the case where the gas compressibility is neglected. In this work the effect of compressibility an the slug length evolution and inlet pressure is computed. Some initial results and numerical approaches are discussed.