In this paper, stochastic Fornberg-Whitham and a stochastic Camassa–Holm (CH) type equations are studied. A Galilean transformation which previously used for a stochastic KdV equation is employed to transform the equations into their deterministic counterparts. Then $(1/G')$-expansion method is used to obtain analytical solutions. 2D, 3D, and contour graphs representing the peakon solutions have been plotted by assigning special values to the constants in the solutions via computer software. In addition, by giving different random values to the external noise, the effect of the noise on the wave-forms has been exhibited. The obtained results have been discussed in detail.