Blebbing occurs when the cytoskeleton detaches from the cell membrane, resulting in the pressure-driven flow of cytosol towards the area of detachment and the local expansion of the cell membrane. Recent experiments involving blebbing cells have led to conflicting hypotheses regarding the timescale of intracellular pressure propagation. The interpretation of one set of experiments supports a poroelastic cytoplasmic model which leads to slow pressure equilibration when compared to the timescale of bleb expansion. A different study concludes that pressure equilibrates faster than the timescale of bleb expansion. To address this, a dynamic computational model of the cell was developed that includes mechanics of and the interactions between the intracellular fluid, the actin cortex, the cell membrane, and the cytoskeleton. The Immersed Boundary Method is modified to account for the relative motion between the cytoskeleton and the fluid. Results show the relative importance of cytoskeletal elasticity and drag in bleb expansion dynamics. Our results also show that a poroelastic model of the cytoplasm can explain experimental data and support the hypothesis that pressure equilibrates relatively fast.