  We develop a framework to understand the mechanics of metamaterial sheets on
curved surfaces. Here we have constructed a continuum elastic theory of
mechanical metamaterials by introducing an auxiliary, scalar gauge-like field
that absorbs the strain along the soft mode and projects out the stiff ones. We
propose a general form of the elastic energy of a mechanism based metamaterial
sheet and specialize to the cases of dilational metamaterials and shear
metamaterials conforming to positively and negatively curved substrates in the
F\"{o}ppl-Von K\'{a}rm\'{a}n limit of small strains. We perform numerical
simulations of these systems and obtain good agreement with our analytical
predictions. This work provides a framework that can be easily extended to
explore non-linear soft modes in metamaterial elasticity in future.
