Numerical studies of Electrohydrodynamics (EHD), specially for multiphase flows have been grown in recent years. This phenomenon that has numerous applications in different fields, deals with coupling of hydrodynamics and electrostatics. In this thesis, numerical study of emulsion of drops in a channel under simultaneous effects of electric forces and Poiseuille flow is investigated. The electric field is created by imposing an electric potential difference across the channel walls and the leaky dielectric model developed by Taylor is used to compute the electric force. This force is directly added to the Navier-Stokes equations as a body force. This force can deform the drop in the direction of the electric field (prolate) or perpendicular to the direction of the electric field (oblate) depending on the electric properties of drop fluid and ambient fluid. Also it creates the so called induced electrohydrodynamic flows inside and outside of the drop. First, the numerical method (front-tracking/finite volume) was validated by comparing drop deformation and induced flows with experimental and theoretical results in literature. There is a maximum five percent error between numerical and experimental results for drop deformation that validates numerical method. Then the interaction of drop-to-wall and drop-to-drop is investigated studying the effect of dimensionless numbers. Oblate drops and prolate drops (type I), are always attracted to the walls but prolate drops (type II), are attracted or repelled depending on the initial distance from the walls and their electric properties. Drop-to-drop interaction depends on the initial configuration of drops in the domain. Drop pairs that have an angle with respect to the direction of the electric field, are always attracted towards each other. If they have an initial separation distance in the direction of the electric field, they attracted to the walls or to each other depending on their separation distance. Prolate drops (type II) have a different configuration in their final state. they may stick together or have a small separation distance, depending on their electric properties. Decreasing the Ohnesorge number, decreases the time required for drop pairs to reach steady state configuration. Increasing the electric capillary number, changes the vertical and horizontal separation distance of drop pairs in steady state configuration, and decreases the time required to reach steady state configuration. The behavior of emulsion of drops is studied by considering oblate drops, prolate drops (type I) and prolate drops (type II). All drops form fiber chains in the direction of the electric field that will break in stronger Poiseuille flow. Oblate drops settle on the walls but prolate drops form chains of fibers that sometimes extend between the walls. Presence of drops will reduce the flow rate of the channel but the flow rate is smaller for prolate drops because oblate drops are settled on the walls. Keywords: Electrohydrodynamics, Oblate / prolate drops, Electric capillary number, Electric conductivity / permittivity, Induced electrohydrodynamic flows, Dielectrophoretic effects