The paper presents developed placement algorithms that allow solving the problem of optimized placement of a given set of flat objects, taking into account additional restrictions specified when arranging real objects in cutting and packing problems. The proposed algorithms are based on the use of the author’s model of potential containers, which describes the free space used for placement in the form of a set of rectangular areas. In this case, objects of complex geometry are considered rasterized in the form of orthogonal polyhedra. A description of the algorithm for setting individual indents for all placed objects is given, restricted zones are introduced, an algorithm is proposed for uniformly arranging a set of objects in the placement space, a placement algorithm is described taking into account several starting points for placement, a speed-optimized algorithm for placing orthogonal polyhedra is proposed, and the procedure for selecting an angle of objects to be packed is described. Examples of various placement schemes obtained using the developed algorithms are given.