We investigated numerically effects of the capillary number, the droplet size and the viscosity ratio on the transient stress responses of a Newtonian droplet suspended in a Newtonian liquid in a sliding bi-periodic frame that represents a flow of two dimensional droplet emulsions in simple shear flow. Understanding the relationship between the droplet deformation and the transient stress responses such as the bulk shear stress and the first normal stress is particularly emphasized, using this computational model problem, where the rheological properties of medium and droplet fluids and flow conditions can be accurately controlled.