We present a theoretical study of the ambient refractive index sensing characteristics of long period gratings in bare and metal-coated D-shaped fibers. An equivalent rectangular core waveguide method based on the first-order perturbation theory has been used to study the modal behavior of the waveguide. Power coupling corresponding to dual resonance in both cases has been investigated, and an optimum metal thickness giving maximum sensitivity has been found to exist. The study shows that the dual resonances can be shifted to lower wavelengths by increasing (decreasing) the metal thickness (core to flat surface separation). Further, an optimum combination of metal thickness and core to flat surface separation, corresponding to maximum sensitivity, has been presented for different cladding modes and their relative performance has been discussed. It has been shown theoretically that detection of refractive index changes as small as $1.67\times {10}^{-7}\mathrm{RIU}$ in the ambient region is possible using the optimized parameters. The study should find application in realizing highly sensitive biochemical sensors.