Commercial-scale development of CO2 geological storage necessitates robust and real-time monitoring methods to track the injected CO2 plume and provide assurance of CO2 storage. Pressure monitoring above the injection zone is a method to detect potential CO2 leaks into overlying formations. We present a generic CO2 storage model with a single injector to predict pressure changes above the caprock due to both fast hydraulic communication and partially undrained loading, the latter often neglected in reservoir simulation. The simulation used a compositional simulator coupled with geomechanics to solve the poroelastic equations in the entire storage complex. The results show that changes of pore pressure above the caprock caused by partially undrained loading reach up to ~15 kPa within ~10 days followed by a gradual decay with time. This is about 1% of the pressure increase in the injection zone. Furthermore, the pressure changes above the caprock are closely related to the advance of the CO2 plume. The results also include forward simulations considering the presence of: a fault either with high or low permeability, a poorly isolated abandoned well, a leaky injector, and a second injector. Fluid flow through high permeability paths across the caprock favors a ~one order of magnitude higher, yet more gradual pressure increase than the base case with a fully covering caprock. Pressure monitoring above the caprock is a feasible technology to track the CO2 plume, requires high precision pressure measurements, and must account for partially undrained poroelastic loading to interpret correctly measured pressure signals in the field.