A newly developed molecular dynamics code was used to study the effect of free surfaces, grain boundaries and voids in the process of melting. It was found that conventional “thermodynamic melting” occurs via nucleation of the liquid at the extended defects with subsequent growth into the crystal. In the absence of interfaces, or when this transition is kinetically hindered, however, a second type of melting transition can be triggered by an elastic instability first described by Born (“mechanical melting”). It is suggested that the distinct characteristic features associated with the two types of melting are actually observed in solid-state amorphization experiments. A unified thermodynamics-based description, in the form of an extended phase diagram, of melting and solid-state amorphization is proposed which brings out the parallels between these two phenomena and suggests that their underlying causes are apparently the same. By investigating the effect of surface stresses on the structure and elastic behavior of free-standing thin films, we discuss how these concepts need to be modified in thin-film and small-grained materials.