In this paper, the process of tsunami wave propagation along the waveguide with flat sloping sides is studied using the wave-ray method. When propagating along the waveguide, a single tsunami wave transforms into the wave train. The expression for the propagation velocities of the fastest and slowest signals is defined. The tsunami waves behavior above the ocean bottom ridges which have different model profiles is numerically investigated with the help of the finite difference method. Results of numerical experiments show that the highest waves are detected above the ridge with flat sloping sides.