Can planes flap their wings like birds? Birds use their strong breast muscles to flap their wings and give them the thrust to move throught the air and fly. In a way, birds use a swimming motion to get the lift needed to fly. Plane wings have a similar shape as bird wings, but instead of flapping their wings, we use engines to thrust them into the air and create the lift needed to fly. (Source)


Can we design an aircraft which could also "flap" its wings to fly?
Yes, we would need fuel to anyways do that.  But, from a design point of view, is it possible to do that?
From a biological point of view, flapping wings is a viable means of flight. However, this presents some problems when scaled up for human flight.

One issue is the square-cube law: as the wings are scaled up, the area scales as a square (relating to lift), but the volume scales as a cube (relating to weight). This means the wings increase in weight faster than they increase in lift, resulting in less effective wings. The higher weight presents issues in making them flap.

ratchet freak pointed out that we do have such machines, and they are called ornithopters. Although there is some potential at smaller sizes (for small UAV's), the weight and force issue prevents them from being very useful at larger scales. Ornithopters were some of the first unsuccessful designs for heavier than air flight.

The best solution we have found is propellers. This doesn't work as well as biological propulsion, but it's much easier to spin a prop than flap the whole wing, and works much better for the larger scales we need to move humans. Flapping is also not effective for reaching higher speeds.

You can also see from the biological side that there is a size limitation. The largest birds are much smaller than our airplanes.