This paper provides the results of a numerical analysis on sound transmission loss of a thin aluminum plate. The finite difference time domain (FDTD) method is used in this study because it simultaneously solves both sound wave propagation in fluid and elastic wave propagation in solid. The calculated value of sound transmission loss gives good agreement with that of mass law. Sound transmission of saw-shaped wave approximated by the sum of sine waves is also calculated. As a result, it is considered that even if a non-linear sound wave reaches to a thin plate, its high frequency components are reduced and the transmitted wave can be treated as a linear wave under the condition which an incident plane wave transmits to infinitely large thin plate.