Layout problems of compressible objects (known also as deformable, elastic, soft) that may change their shapes to better hosting in the optimized container have a wide spectrum of applications, in particular, in land allocation, floor planning, logistics, material sciences, biology, mechanics, nanotechnologies. The paper focuses on the study of porous media where elements can be deformed by external force however the mass of each individual element remains unchanged. A problem of layout of particles in a rectangular fragment of the porous media under pressure is formulated. Particles are approximated by polygonal objects of variable shapes with respect to a given limits of metric parameters under area and convexity conservation. Free translations and continuous rotations of the particles are allowed. A multistart strategy is used for finding local optimal solutions of the problem. It combines a feasible starting point algorithm, using packing original polygons in a fixed container and a decomposition procedure for packing compressible objects in a minimal height container. Computational results for the real data example are provided.