The "collector" method of uniaxial dry compacting homogeneously dense powdered bodies of complex shape without macroscopic defects has been developed. It was based on the selfalignment of uniform density regions within a green compact by design of special mold to reduce die-wall friction effects. An equation was proposed that determined the density differential throughout the height of a green compact, which depended on geometrical parameters, and required the controlled movement of die parts. The technique of pressing with the collector method has been developed and patented by TPU. Based on the principles of the collector method a compaction mold of spiral type was modeled for compaction of cylindrical compacts with two alternating, oppositely-moving parts of the passive shaping surface with sliders, twisted at an angle of 36 degrees. The process of powder compaction was simulated by finite element method. The simulation results of the deformation process in the compacts showed that the density of each layer distributed irregularly with the curvature of isosurfaces in the direction of movement of the punch. The results of comparative simulation showed that the statistical dispersion of local values of the deformation of the green compacts made by collector method with the mold of spiral type is reduced to 48% when compared with conventional static compaction and reduced to 5% when compared with collector compaction using the mold of non-spiral type. This method decreases the density gradients. It can be applied to manufacture ceramic articles from nanopowders like impellers and plates with longitudinal holes.