Technological advancement has made manufacturing of various nanostructures possible. Thermal transport in such nanostructures is fundamentally different from macroscale. Initial studies have indicated that thermal properties of these nanostructures also depend on its geometry. Hence, it is possible to tailor nanostructure geometry to achieve targeted thermal properties. In the present work, thermal transport in (a) constricted thin films and (b) constricted nanowires is studied using gray phonon Boltzmann transport equation (BTE) for a wide range of constriction ratio. Finite volume method is used to numerically solve the BTE with the relaxation time approximation. We show in this paper that by varying the degree of constriction, thermal conductivity of thin films and nanowires can be altered significantly. Thin films and nanowires are found to respond differently to constriction.