Several building projects require deep foundations, particularly for huge structures such as bridges and skyscrapers. A typical type of deep foundation is the caisson, a massive watertight chamber that sinks into the ground, onshore, or offshore, to build a robust substructure which can be used for temporary and permanent works. The tip of the caisson is normally tapered  on the inner edge to facilitate the sinking. Sinking an offshore caisson is a complex, kinematic procedure that demands specialized knowledge and experience to conduct safely and adequately. The study explores the challenges in the analysis of sinking caissons using various analytical methods and arrives at a method of feasibility study of the caisson sinking process for projects. A case study is presented to demonstrate the procedure developed in the study. The feasibility study for caisson sinking problems comprises an evaluation of site lithology, caisson design, sinking methods, environmental issues, and cost analysis. The bearing capacity analysis is performed for the caisson, and a factor of safety for sinking for limiting conditions against the working load is evaluated for the caisson in different soil strata and underwater depths. The kinematics of sinking at each depth is captured in the proposed method by considering distinct earth pressure coefficients for internal and external soil. The study would assess the various sinking techniques available for caissons, such as dredging, bentonite circulation, water jetting, and excavation, and determine the most appropriate technique depending on site conditions, caisson type, and its design. The conclusions of this study offer a simple analytical methodology to evaluate the feasibility of the caisson sinking for engineers and construction professionals under given conditions.