An extended unsteady vortex-lattice method is developed to study the aerodynamics of insect flapping wings while hovering and during forward flight. Leading-edge suction analogy and vortex-core growth models are used as an extension, which is incorporated into a conventional unsteady vortex-lattice method in an effort to overcome the challenges that arise when simulating insect aerodynamics such as wing-wake interaction and leading-edge effects. A convergence analysis was carried out to derive an optimal aerodynamic mesh and a time-step size for flapping-wing models. A parallel computing technique was used to reduce computational time. The aerodynamics of hawkmoth (Manduca sexta) wing models was simulated, and the results were validated against previous numerical and experimental data.