Abstract: This paper deals with the non-linear propagation of sound waves radiated by a thin spherical shell vibrating in ideal fluid.Non-linear sound field is obtained by the method of renomlization proposed by Keily and Nayfeh,and the structural response of the spherical shell considing of the acoustic load is obtained using Junger and his cooperators'spherical function expansion.Here,for a spherical shell exicited with various force distributions and frequencies,we combine the above.methods to calculate the structural responses,the wave forms before the formation of shock wave,and the first two order waves (including the lst and 2nd harmonic waves,sum and difference frequency waves) which wary with the exciting frequency (frequencies),radial distance and directions.Comparing our computing results with linear theoretical values,we analyse the rules of generation and propagation of non-linear waves.