In this theoretical study, we have chosen to use a body of an ellipsoidal geometric form as an
indenter, where we determined the mathematical expression of the static hardness as function of the
depth and the radii of the area of projected imprint. We used the general formula of the static
hardness expressed by the ratio of a force applied perpendicular on the indenter to the resulting
area of the imprint; also, we have established the real imprint (cap) of an indenter of revolution
ellipsoid form. Finally, geometrical and mathematical approaches have been used to derive the
formula of the static hardness expression.