Handling and manipulating flexible porous objects is one of the main challenges in robotics for household and industrial tasks. Improving the design of grippers for flexible objects of manipulation is an important stage in the development of this topic. This article proposes a method of modeling a gripper for porous objects using the finite element method. It identifies the main parameters of the model that will affect the grasping force and the permeability of porous objects. The power characteristics of the obtained gripper model for different supply pressures, with varying porosity of the manipulated objects, are determined. The obtained characteristics are then used to find the correspondence of channel length for three textile materials with different permeable properties. An experimental study of the lifting force is conducted, and a comparison is made with the obtained modeling data for the presented samples. Additionally, using the obtained simulation data, an analysis of the pressure distribution on the surface of the porous object of manipulation is performed. As a result, it is found that the gripping device must use a design with elements to stabilize the distribution of pressure in its chamber, which will increase the stability of the gripping process.