<p>Legged robots have been the focus of many researchers aiming to develop commercially available, stable, and versatile legged robots due to their ability to navigate unstructured environments and perform complex motions effectively. Quadruped robots, a subset of legged robots, stand out for their ability to maintain stable ground contact using multiple points, allowing them to adapt to diverse landscapes and environmental challenges. This paper presents a comprehensive analysis and verification of the kinematics, inverse kinematics, and dynamics of quadrupedal locomotion. Finite element analysis (FEA) using ANSYS is conducted to provide a detailed examination of the structural performance of two quadruped models: Nova and Spot Mini. A mathematical derivation of the kinematics and inverse kinematics is presented and verified using Peter Corke’s Robotics Toolbox in MATLAB and the Gazebo physical simulator. To fully analyze the locomotion of quadruped robots, a comparative analysis is presented on different dynamical models, including the rigid body model, centroid model, single rigid body model, and linear inverted pendulum model (LIPM). The results of the FEA concluded that Spot Mini demonstrated higher stress tolerance and deformation resistance compared to the Nova model. The verification of kinematics and inverse kinematics illustrated the most stable base height of the robot, based on the error calculated from the theoretical models and the physical simulator using the rigid body dynamical model of a quadruped robot.</p>