A　transient　phase　field　model　is　developed　of　droplets　and　bubbles　in　viscous　fluids　subject　to　an　external　electric　field.　The　model　is　transient　and　fully　three-dimensional.　It　is　based　on　the　explicit　finite　difference　solution,　enhanced　by　parallel　computing,　of　the　coupled　nonlinear　governing　equations　for　the　electric　field,　the　fluid　flow　field　and　free　surface　deformation.　The　effect　of　mesh　size　and　interfacial　thickness　on　numerical　accuracy　and　stability　of　the　phase　field　modeling　is　studied.　The　phase　field　model　is　validated　with　the　Taylor　theory　for　the　deformation　of　a　single　dielectric　droplet　in　electric　fields.　Computed　results　show　that　the　deformation　of　a　leaky　dielectric　droplet　undergoes　various　different　deformation　stages　before　reaching　the　equilibrium　oblate　shape,　which　is　caused　by　the　free　charge　relaxation　near　the　fluid-fluid　interface.　Also,　the　deformation　and　rising　speed　of　the　bubble　are　affected　by　the　applied　electric　field　in　both　magnitude　and　direction.　For　a　rising　bubble　in　a　horizontal　electric　field,　it　rises　slowly　as　a　result　of　a　larger　drag　caused　by　electric-stretching　along　the　horizontal　electric　field.　In　comparison　with　the　vertical　field,　the　indentation　on　the　bubble　base　starts　earlier　but　grows　more　slowly　after　an　initial　period.　The　bubble　deformation　and　fluid　flow　structure　in　a　horizontal　field　are　three　dimensional.