A solid bluff object produces a recirculating wake region immediately behind it when subjected to flow separation under a steady flow condition. Similar phenomena can also be observed for a porous body. However, unlike the solid object the porous body allows some part of the flow to go through it. A consequence of this flow penetration in porous objects is, the wake behind the body may get reduced in size and detach from the body. The wake even may disappear at some value of the porosity parameter (Darcy number). In this brief article, we compute the critical values of the porosity parameter for complete disappearance of the wake region behind two-dimensional porous bodies of circular and square shapes. A regime diagram is constructed to show the regions of wake formation, its detachment and finally its disappearance around circular and square shaped porous bodies. The critical value of the porosity parameter increases with increasing Reynolds number, and it is found greater for the square body in comparison to the circular one. The study provides a quantitative estimation of how the porosity plays a significant role in demarcating the flow characteristics around porous objects.