The pressure disturbance propagation through a weakly compressible medium, bound by rigid structure as well as material interfaces, has an important bearing on the safety analysis of liquid-metal-cooled fast breeder reactors. The analyses have been carried out using numerical algorithms based on Eulerian, Lagrangian, or mixed formulations. Even though the results obtained from these schemes compared well with the benchmark experimental results, certain drawbacks, such as less accurate treatment of material interfaces in the Eulerian schemes and mesh distortion in the La-grangian schemes, and so forth, remain. These drawbacks may be overcome by using a method of characteristics in two dimensions known as the near-characteristic method to solve the problem. The region of interest is discretized into Eulerian grids, and the flow parameters are obtained from the compatibility equations corresponding to the near characteristics generated from the grid points. The material interfaces are tracked explicitly, using the near-characteristic scheme. The scheme is used to analyze a typical core disruptive accident problem, and the results are compared with experimental results as well as those ob. tained using two other numerical schemes. Good agreement is observed among the results; indeed, the one-dimensional problem of exploding wire phenomena and the two-dimensional problem of core disruptive accident analysis validate the effectiveness of the scheme. The future extension of the present scheme will include fluid structure interaction and complex internal structures.