Effects of inertia on the rheology of dilute Newtonian emulsion of drops in shear flow are investigated using direct numerical simulation. The drop shape and flow are computed by solving the Navier-Stokes equation in two phases using Front-tracking method. Effective stress is computed using Batchelor's formulation, where the interfacial stress is obtained from the simulated drop shape and the perturbation stress from the velocity field. At low Reynolds number, the simulation shows good agreement with various analytical results and experimental measurements. At higher inertia deformation is enhanced and the tilt angle of the drop becomes larger than forty-five degree. The inertial morphology directly affects interfacial stresses. The first and the second interfacial normal stress differences are found to change sign due to the change in drop orientation. The interfacial shear stress is enhanced by inertia and decreases with capillary number at lower inertia but increases at higher inertia. The total excess stresses including perturbation stress contribution shows similar patterns. (c) 2005 The Society of Rheology.