Deep geological formations, such as saline aquifers, unmineable coal seams, and depleted hydrocarbon reservoirs, offer a great potential for large-scale underground storage of carbon dioxide (CO2). Well injectivity, formation storage capacity, wellbore integrity and caprock integrity are among critical topics in CO2 underground storage. This work focuses on constraints imposed by the wellbore stability and caprock integrity on the wellbore injectivity. The buildup of bottom hole pressure, the evolution of CO2 plume, and the distribution and evolution of pore pressure in the geological formation are predicted using semi-analytical solutions. The disintegration risk of wellbore is assessed with updated bottom hole pressures at various injection times. The caprock integrity is evaluated by applying the evolving vertical total stress in the saline aquifer in contact with the caprock at the bottom of caprock layer to assess the risk of fracturing in caprock.