We report experimental results on the deformation of a single drop suspended in a medium under uniaxial elongational flow along the central axis of a converging conical channel made of Plexiglas. Both the drop and the continuous phases consist of constant viscosity elastic fluids, so-called Boger fluids. This study reveals several interesting features about the role played by both the drop and matrix elasticities on the drop deformability. In a given matrix fluid, the drop deformation decreases as its elasticity increases. For a given drop fluid, the matrix elasticity has the opposite effect: the drop deformation increases with increasing matrix elasticity. An empirical relation between the drop and matrix deformations is established as a function of the drop and matrix characteristic elastic times.