Autonomous robots are employed in several important tasks, for example, from health care to military and defense applications involving operations in hazardous and inaccessible environments. Legged autonomous robots can be advantageous due to high adaptability and stability over any terrain, superior obstacle avoidance capability, and advantages through redundancy by utilizing multiple legs. Compared to rigid-legged robots, flexible-legged robots are highly compliant, suitable for non-destructive inspection applications, and possess enhanced gait control with improved energy efficiency. An approach to designing flexible-legged robots is to mimic desirable features evolved via natural selection in biological organisms. Conceptualizing new biologically inspired flexible-legged robots can expand the usability and improve the efficiency of robots in different applications. In this project, the inspiration for locomotion design is the mobility principle utilized by small-scale organisms in the form of beating protrusions referred to as cilia or flagella. Notably, the collective beating dynamics of ciliary arrays reveal essential characteristics such as synchronization, phase locking, and metachronal coordination suitable for terrestrial and aquatic robot locomotion. This thesis presents the formulation, simulation, and analysis of a planar bio-inspired flexible-legged robot for terrestrial locomotion. Each leg of the robot is modeled as a bundle of flexible filaments using constrained Euler elastica that is suitable to describe some of the characteristics of cilia or flagella. The legs/protrusions are mechanically coupled through the base, representing the robot's payload, via linear springs or elastic lumped elements, to produce certain desired collective beating patterns upon individual moment actuations. The locomotion mechanism is illustrated in simulation, wherein the results pave the ground for future work with refined modeling to account for hardware implementation constraints.