The problem of a single drop immersed in a flowing immiscible fluid is here investigated for non-Newtonian fluids in slow, steady-state flows. The two materials are assumed to be second-order simple fluids, hence effects of constitutive elasticity are included in the analysis. A perturbative approach is used to obtain the complete analytic solution, including the drop shape, up to second order in the imposed deformation rate of the external flow. The adopted perturbation method differs from the classical one adopted for the Newtonian case, as it makes use of rotational invariance to obtain from the start a workable tensorial representation of the pressure and velocity fields, and of the drop deformation.