This paper studies the feasibility of using the nonlinear model predictive control as a formation flight control algorithm for unmanned aerial vehicles. The optimal control inputs for formation flight are calculated through the cost function which incorporates the relative positions of the individual vehicles to maintain a desired formation and also the inequality constraints on inputs and states using the Karush-Kuhn-Tucker conditions. In the nonlinear model predictive control setting, the optimal control inputs are implemented in a receding horizon manner, which is suitable for dealing with dynamic constraints. Numerical simulations are executed for the validation of the proposed scheme.