Calculus of variations is applied to the problem of optimal mixing of two immiscible fluids in a laminar flow where stretching of the interface between the liquids is treated as an objective function. Under the action of an optimal control, the system behaves like that driven by a negative surface tension, i.e., an initially flat interface evolves in long tongues that are stretched and twisted by the flow. The method was tested for mixing by Stokes flow in lid-driven two-dimensional rectangular cavity.