Abstract: The aim of the paper was the numerical investigations of the finite amplitude waves interaction in water. The problem was considered as an axial symmetric one. It was assumed that circular piston and ring-shaped piston were the source of two different frequency finite amplitude waves. The mathematical model was built on the basis of the Khokhlov - Zabolotskaya - Kuznetsov (KZK) equation. To solve the problem the finite-difference method was applied. The mathematical model and some results of numerical investigations are presented. The spectrum of the wave for fixed distances from the source, the pressure amplitude changes for different frequency waves as a function of distance from the source and pressure amplitude distribution for fixed distances from the piston were investigated.