The more cost-efficient way of creating new materials with improved properties is to blend two or more existing materials. The properties of blends are directly related to their morphology, which changes during processing as a result of phase deformation, breakup, and coalescence. Study of deformation and breakup of a single droplet dispersed in a different immiscible liquid is an essential step to understand the rheology of immiscible blends. To understand dynamics of drop deformation, simulation tools could be useful tools to discover the effects of rheological properties like viscoelasticity. In this work; deformation of a viscoelastic drop in a Newtonian matrix under Stokes flow is simulated using a eXtended finite element method (XFEM). We consider the matrix inside a continuous mixer (like twin screw extruder), where shear and elongational flows are presents. Surface tension is included in the traction vector across the interface between the droplet and the matrix. The governing balance equations are solved once over entire domain (droplet and matrix). The surface of droplet is described by a discretized mesh and its position is updated by tracking the nodal positions in time. For XFEM integration, the position of the surface is determined explicitly by a numerical level set. In order to couple the velocity between droplet and matrix, a constrain is applied on balance equations. Constraints are enforced using a Lagrangian multiplier and also using weak interface conditions. Results are discussed for different viscosity ratio's, different capillary numbers and different Deborah numbers. The influence of viscoelasticity of drop like relaxation spectrum and different viscoelastic constitutive equations on the drop deformation process was discussed.