The purpose of this paper is twofold: first, it aims to characterize plastic flow and ductile fracture in sheet-bulk indentation and, second, it proposes a closed-form analytical framework that can be easily applied to estimate the through-thickness pressure and force that needs to be applied by a flat compression punch as a function of the geometry, the mechanical properties of the blanks and the friction along the blank-tool interfaces. The methodology combines experiments with properly designed tool systems, which facilitate or constrain material to flow sideways (in the direction of the length), and analytical developments build upon the upper bound method for upsetting, transition to die filling and die filling of sheet-bulk compression by a flat punch. Experimental work with aluminium EN AW-1050A shows that depending on the geometry of the punch, the physics of sheet-bulk indentation may exclusively involve plastic flow or may result from a combination of plastic flow and fracture to detach surfaces from the neighbouring regions of the blank through controlled crack propagation. Results also show that the mechanics of sheet-bulk indentation can be easily and effectively analyzed by means of sheet-bulk compression under plane strain conditions.