The effect of matrix elasticity on the break-up of an isolated Newtonian drop under step shear flow is herein presented. Constant-viscosity, elastic polymer solutions (Boger fluids) were used as matrix phase. Newtonian silicon oils were used as drop phase. Three viscosity ratios were explored (drop/matrix), i.e. 2, 0.6 and 0.04. Following the theoretical analysis of Greco [Greco F (2002) J Non-Newtonian Fluid Mech 107:111-131], the role of elasticity on drop fluid dynamics was quantified according to the value of the parameter p=tau/tau(em), where tau is a constitutive relaxation time of the matrix fluid and tau(em) is the emulsion time. Different fluids were prepared in order to have p ranging from 0.1 to 10. At all the viscosity ratios explored, break-up was hindered by matrix elasticity. The start-up transient of drop deformation, at high, but sub-critical capillary numbers, showed an overshoot, during which the drop enhanced its orientation toward the flow direction. Both phenomena increase if the p parameter increases. Finally, the non-dimensional pinch-off length and break-up time were also found to increase with p.