The finite element model of transient pressure pulse propagation in a pipeline is presented in the form of the standard structural dynamic equation, which combines steady flow analysis for obtaining the initial conditions of the flow in the form of pressures and flow rates and non-linear dynamic analysis by using explicit numerical integration techniques. Three options of simplification of governing equation set have been analyzed. At low values of steady flow speed many non-linear and convection terms could be omitted, while at the flow speeds comparable with the wave propagation speed the full equation system has been analyzed. The full equation system analysis involves the techniques ensuring corrections of the initial conditions and of the nodal flow rate balance. The investigated pipelines may contain large number of branches and loops. Parts of large pipelines are analyzed as separate sub-models by employing non-reflecting boundary conditions at the cut boundaries. Properties of pressure pulse front degradation as it propagates through branching points of the pipeline can be examined. Keywords: finite element methods, compressible flow, dynamical systems.