The method for estimating a tsunami height using the wave front kinematics computation has been developed and tested. This method is based on an orthogonal advance of computational points located along a moving tsunami wave front line. Precise algorithms for determining these points movement direction and an addition of new ones have been proposed. This method was tested in an area with a constant depth. Then in the areas with a parabolic and sloping bottom topography the obtained result of wave front propagation was compared to exact analytical solutions, which are delivered to such depth models. The method proposed makes possible to compute not only tsunami travel times but wave rays as well. Tsunami amplitudes can be estimated by the wave-ray divergence and a change in depth along the wave route. The wave amplitude estimation was tested against the results of the shallow-water numerical modeling of tsunami propagation using the MOST software. A difference in results between the two methods on the model (slope-like) bathymetry does not exceed a few percent. The advantage of the method proposed is its rapidness and low computer costs.