One of the critical problems in the design of autonomous insects is power consumption. The independent control of several legs is energetically expensive, while the energy capacity of typical electrochemical batteries is quite small. The net result is autonomous robotic insects that have extremely limited range. The authors propose an alternative approach to this problem that enables autonomous robot insects that exhibit extremely high movement efficiency, and thus are capable of long range missions. Specifically, the desired limb motion is obtained by designing a lightly damped skeletal structure and exciting the skeletal structure at an appropriate resonance. The approach is called elastodynamic locomotion. Rather than altering the open-loop dynamics of the machine, as is the case with conventional-scale machine control, the control actuator serves only as an excitation source that excites the open-loop dynamics of the skeleton structure. Since the motion of the insect limbs operate at their structural resonance, the acceleration and deceleration for each motion (i.e.: stride for a walking machine) requires no power, which results in a highly efficient machine. Since the motion of the insect limbs is determined by design and not by control, the primary focus of this work is in the design of a skeletal structure that will exhibit walking motion when vibrationally excited. This paper presents various insect designs that will generate a walking or flying motion with minimal actuation.