This paper presents a wave propagation analysis method for a periodic railway track having a finite irregular zone. A half-infinite periodic sub-region is represented by an impedance matrix. The infinite system is reduced to a matrix equation with finite DOF by coupling the impedance matrices with the irregular zone. Through numerical examples, influence of the heterogeneity on the wave propagation is discussed in terms of the dispersion of wave modes. It is found that the irregularity is effective to cut off the wave transmission.