A soft drop is often used as a mechanical model for a cell with a viscous cytoplasmic fluid inside. For example, a polyelectrolyte gel has been proposed as a model for the viscous fluid inside biological cells. In this work we focus on a soft porous drop and introduce a continuum model to study the velocity field around a soft porous drop in simple flows such a uniform streaming flow and a linear shear flow. We illustrate how the flow depends on the mechanical properties of the soft solid such as porosity and deformability. Extension to active stress from the soft solid will be incorporated.