Classical continuum mechanics often neglects the contribution of interfaces to the deformation of solids. This is usually reasonable for stiff (e.g. crystalline) materials, whose elastic energy of the bulk almost always overwhelms contributions from the surface except for very small objects that are hardly measurable. However, for compliant materials such as elastomers and hydrogels, solid surface tension can play an important role in either driving or resisting their deformation at relatively large length scale that is well within the continuum description. With applications ranging from MEMS (Micro-Electro-Mechanical System) to drug delivery, from soft robotics to biomimetic systems, it is of great technological significance to understand the underlying mechanisms of the deformation in these compliant elastomers and gels in a quantitative manner. It is for this reason, we attempt to develop theoretical and numerical models to capture the coupled effect of surface tension and elasticity in deformation of compliant solids. In this dissertation, I present our theoretical and experimental understanding of the effect of surface tension as it applies to a variety of phenomena involving deformation of compliant solids. Chapter 1 constructs a deformation map in which shape change of an elastic solid is captured by two dimensionless material parameters with a simple scaling argument. To enable accurate predictions, a finite element modelling technique, which incorporates surface tension effect, is used to quantify the shape change of a free standing elastic solid circular cylinder driven by both gravity and surface tension. Chapter 2 and 3 outline two independent approaches of measuring surface tension of a solid by monitoring its deformation. Chapter 2 describes a method that is applicable to materials with a low moduli (less than 100 kPa). We mould gelatine against patterned master surfaces. The sharp features on gel surface are rounded compared to the master and can be significantly flattened upon demoulding. We model this phenomenon using finite element technique as an elastic deformation driven by surface stress, and thus estimate the values of the solid-air surface tension of these gels. It is however limited when apply this method to stiffer materials, for the bulk elasticity in these materials often dominates the deformation. An alternative technique of surface tension measurement described in Chapter 3 is specifically designed for not-so-compliant materials with moduli larger than 100 kPa. A thin solid film is deflected with a rigid indenter and its deflection can be modelled using a version of nonlinear von Karman plate theory incorporating surface tension. We apply this method to polydimethylsiloxane (PDMS) and obtained a value of its surface tension consistent with that reported in the literature. Chapter 4，5 and 6 study the mechanics of contact and adhesion between solids, in which classical theories are extended to include surface tension of the solid surfaces outside the contact region. Chapter 4 models the adhesive contact between an elastic half-space and a rigid sphere in the absence of external load. We present a finite element solution of such a problem, which shows the transition between classical Johnson-Kendall-Roberts (JKR) deformation and surface-tensiondominant deformation. Chapter 5 extends the problem to include non-zero external load as well as non-adhesive contact. Besides the contact configuration of a rigid sphere and elastic half space, we also simulate contact between an elastic sphere and rigid plates. Both frictionless and no slip contacts are modelled and the results are compared to provide some insights on the effect of interface conditions. We also assess the validity of Hui et al.'s (2015) small-strain theory on contact of soft solids, which includes surface tension effect, in large deformation regime. Chapter 6 focuses on modelling the surface displacement of the elastic substrate when being indented by a rigid sphere. Using the same FEM model from the previous two chapters, we compare the modelled surface profile of the substrate to an experiment performed by Jensen et al. (2015). Chapter 7 lists some suggestions for future work.