Abstract We present results from modeling the deformation of a viscoelastic drop suspended in another viscoelastic fluid subjected to uniaxial extensional flow using the DEVSSG-FEM. Viscoelasticity is implemented using the Oldroyd-B constitutive relation for both the drop and surrounding matrix fluids. To allow efficient solution of the discretized problem, we employ an implicit temporal integration scheme with an accelerated quasi-Newton method. Important viscoelastic effects for both drop deformation during extensional flow and drop retraction following cessation of flow are elucidated. Viscoelastic drops in a Newtonian matrix lengthen less at steady state extension than Newtonian drops because of the accommodation of stress by elasticity. However, the stored elastic effects cause rapid tip retraction during the recovery of polymeric drops. Drops stretched in a viscoelastic exterior flow are enhanced in length compared to those in a Newtonian matrix because of first normal stresses from the matrix. During recovery, drops in a viscoelastic matrix can exhibit significant lengthening upon cessation of extensional flows, causing additional strain before retraction. This behavior is strongly dependent on the details of the exterior flow.