This dissertation studies several elasto-capillary phenomena. We first experimentally demonstrate that the coupling of familiar liquid/air interface tension and elasticity can be used to drive droplet motion. Specifically, we show that droplets placed on different sides of a thin elastic film tend to repel each other. An evaluation of the intermediate state energy is carried out to explain the phenomenon and a “satellite” droplet pattern is designed and observed. In a separate experiment, we put a droplet on a fibrillar structure terminated by a thin film and find that the droplet move spontaneously and chaotically. The surface tension of the droplet cause a significant deformation of the substrate and generate a periodic driving force. This periodic driving force together with evaporation induce an instability of the droplet that cause the spontaneous chaotic motion. The second part of this dissertation aims to extend the classical adhesive contact and fracture mechanics theory to include the effect of surface tension. Specifically, we consider the contact between a rigid spherical/cylindrical indenter and an elastic substrate. The surface of the substrate has both adhesion and surface stress included. We also study the effects of surface tension on mode-I cracks and find that the linearization of curvature is not valid near the crack tip because of the singularity. Using an asymptotic analysis, we show that surface tension can reduce the energy release rate which is consistent with our own finite element calculations. Finally, we consider the effect of solid surface stress on problems with large deformation. A closed-form large deformation solution is found for the pure bending of a long plate. We find that surface stress can significantly increase the bending stiffness and we also discover an instability under load control. In Chapters 8 and 9, we use a large deformation finite element method to study the effect of surface stress on a penny-shaped crack inflated by internal pressure and the contact between a rigid circular punch and an elastic substrate. Our results suggest that surface stress can resist deformation and reduce energy release rate.