In this paper, some exact solutions of the stochastic generalized nonlinear shallow-water wave
(SGNSWW) equation are obtained. This equation is an important equation in fluid mechanics field. Opposite
to what is usually assumed in the literature, the coefficients of the nonlinear terms in this stochastic
nonlinear partial differential equation (SNLPDE) are considered to be random quantities. The random
variable transformation (RVT) technique is combined with the modified extended-tanh function method
(METFM) to get the stochastic solutions represented by the probability density functions (PDFs) of the solution
processes in terms of the PDFs of the random coefficients. These solutions are illustrated graphically
along the spacial and time dimensions at a certain wave speed.