Blockage in pressure pipelines has become a serious issue in the world. According to the basic principle of auto-oscillation theory, the simplified model is put forward for the numerical simulation of blockage detection. Based on the theory of transient flow, the governing equations of transients in a pipeline including blockage are established with the adoption of Dirac delta function. Non-dimensionalizing and linearizing the governing equation, the equations will be simplified. An analytical solution has been deduced under the fixed boundary conditions. By Fourier series analyzing, the amplitudes of each harmonic component in different periods are calculated, and the damping exponent of each harmonic component can be obtained. The results show that the blockage damping is direct ratio to the flow rate of pipe, and the location of damping has the cosine relation with damping parameters, so the location and magnitude of blockage can be fixed if two blockage damping parameters are known.