Nanowires and in general nanostructures present surface energy that makes their properties size-dependent. Using first principles (Hartree-Fock and Denisity Functional Theory) methods, we have calculated piezo-electric and elastic properties of wurtzite [0001] nanowires, in particular ZnO and AlN nanowires. For ZnO, we have studied the effect of partial substitution of zinc by mercury and found that this leads to the significant enhancement of piezo-electric properties. For aluminium nitride, we have further built a classical, Finite Element (FEM), model of a nanowire, using the bulk and surface energy model with parameters derived from ab initio calculations. The elastic properties obtained with the FEM model compare very well with those obtained with the full ab initio calculations. The FEM continuum model can be used to model similar nanostructures in ranges of sizes or geometries where ab initio calculations are not possible, and also to predict the bending or twisting properties of nanowires where ab initio methods are not yet available.