Embossing of metallic glass supercooled liquids into templates is emerging as a precision net-shaping and surface patterning technique for metals. Here, we report the effect of thickness of metallic glass on template-based embossing. The results show that the existing embossing theory developed for thick samples fails to describe the process when the thickness of metallic glass becomes comparable to the template cavity diameter. The increased flow resistance at the cavity entrance results in viscous buckling of supercooled liquid instead of filling. A phenomenological equation is proposed to describe the thickness dependent filling of template cavities. The buckling phenomenon is analyzed based on the folding model of multilayer viscous media. We show that controlled buckling can be harnessed in the fabrication of metal microtubes, which are desirable for many emerging applications.