In the present paper we consider a mathematical model of the motion of particles in the surface air layer under the influence of sudden gusts of wind. The equations of motion were used in the Stoke's form. Gusts of wind determine the nonsmoothness of the velocity field, which can be modeled using the Heaviside function. For a number of parameters, a simulation of the particle's waning is performed, the complex nature of the trajectory is reflected. The results of the calculations show the significant influence of the nonsmooth velocity field on the qualitative behavior of particle motions.