A process of self-assembly induced by electro-chemical etching was used to produce nano and micrometer scale pyramid-structures on (100) surfaces of gold. The pyramids grew in a self-similar fashion with the facets aligned in (114) plane. Using the unique characteristics of the self-similar pyramid structure, plastic compression of the pyramids by a flat-surface platen was performed to study length scale effects in the plastic deformation. A continuum limit analysis and a finite element simulation as well as molecular dynamics simulations were carried out to predict the deformation and load-displacement behavior of the pyramid compression. The limit analysis predicts that the load of compression is proportional to the square of the contact-compression displacement. The continuum analysis provides estimation on the asymptotic behavior of the elastic-plastic load-deflection response of the pyramid under compression for a large value of displacement. The three dimensional molecular dynamics simulation was utilized to study the dislocation activities during the early stage of the pyramid compression. Experiments were also carried out by pressing the pyramids with an atomically flat mica surface. The deformation of the compressed pyramid was measured using an Atomic Force Microscope (AFM). The continuum analyses predict size independent values of the slope change of the pyramid facets near the contact edge, caused by plastic deformation. However, atomistic simulation predicts an opposite value of the slope change to the prediction of the continuum analyses. The AFM measurements of the slope change show size dependent transition from the prediction of the continuum analyses to that of the atomistic simulations. The transition data provide an apparent characteristic length of the size dependence of plastic deformation in a small volume. Molecular dynamics show that at very small length scale the size effect is strongly influenced by surface adhesion effects.