The dynamics of viscous droplets near solid surfaces, especially micro-textured surfaces, and the interaction between them are of great importance in industrial applications, biochemical processes, and fundamental materials research on surface wettability. In this work, a three-dimensional spectral boundary element method has been employed to investigate the dynamics of a viscous droplet falling under gravity influence to micro-textured solid surfaces. The droplet size, in this study, is comparable to the size of the surface texture. The influences of the Bond number, relative size of the droplet with respect to the surface features, and the topological characteristics of the substrate on the droplet motion and deformation are investigated. The stress exerted on the substrate due to droplet motion is also explored.