When a tsunami wave comes from the ocean and propagates through the shelf, it is necessary to predict the maximum flooding of the coast, the height of the tsunami on the coast, the speed of the tsunami front through the coast, and other characteristics. A linear solution to this problem is unsatisfactory: it gives an infinite rate of coastal flooding, that is, the coast is flooded instantly and without a frontal boundary. In this study, we propose a new solution in nonlinear theory to calculate these tsunami characteristics. The obtained formulas show that the tsunami wave can be stopped on the shelf when approaching the shore. For this, it is necessary to artificially raise several tens of bottom protrusions to the level of calm water. Thus, the obtained solution allows to saving human lives and preventing material damage.