The subject of this study concerns a method of manufacture of porous media for which the solid matrix is capable of experiencing deformation under the influence of the flow field. Conventionally, the matrix design parameters, elasticity and pore geometry, cannot be precisely controlled and the choice of parameters is limited to existing available media. Here a solution is provided that uses an indirect solid-free form fabrication process that combines 3D Printing with an infused Polydimethylsiloxane elastomer to provide a highly deformable matrix with controlled pore architecture. The manufacturing method is presented in detail. Local microscopy analysis of the manufactured matrix shows that the method has a high capability to accurately create pore structures at length scales as low as 0.75 mm. Experimental flow measurements further validate that the intended pore geometry is able to be reproduced in highly deformable matrices. The experimentally determined permeability of the deformable matrix is determined to agree with the intended within 95 %.