The present paper provides a short literature survey of the treatment of particle motion in fluids as a basis of the author’s own work in this field. The work relates to the motion of a small solid particle inside a thin liquid film. The particle motion is treated numerically to provide information of interest to thin film liquid coating. The numerical computations yield information on the local velocity and pressure distributions, but also integral information expressed in drag and torque coefficients. The computations are carried out for stationary flows of low Reynolds and capillary numbers and results are presented for different values of surface dilatation and shear viscosities. Translational and rotational motions of the particle are considered by integrating the resultant second-order partial differential equation with an alternating direct implicit method. The numerical results reveal in all cases the strong influence of the surface viscosity on the motion of the solid particle in the viscous liquid layer when the radius of the particle is of the same order of magnitude as the thickness of the liquid film or when the particle is close to the liquid-gas interface.