The present form and the design of the wheelchair suffer from drawbacks such as movement restricted along flat surfaces only, issues related to stability, and inability to move along the staircases or uneven surfaces. The attempts for getting improved movement of the wheelchair seem to be in the developing stage, and the authors felt a need to design a safe wheelchair to overcome the drawback with a rocker boogie mechanism and relevant analysis of the chair. The present work encompasses a study of a boogie rocker mechanism, design calculation for its implementation in wheelchair applications, and modelling the proposed wheelchair using CAD software. The present work further focuses on calculating stress, strain, total deformation, and frictional stress associated with the designed model. The calculated values of the aforementioned parameters using finite element analysis are in close agreement with their analytically calculated values. Thus, practical execution of the proposed mechanism for field application shows good potential for developing a safe, stable, and all-terrain wheelchair for the patient’s benefit.