This paper proposes a method for determining the mechanical properties (Young's modulus, Poisson's ratio, yield strength, and work hardening factor) of a material at a specific point using an indentation technique that utilizes a specially designed indenter in conjunction with an inverse problem and finite element analyses. The specially designed indenter combines the characteristics of spherical and conical indenters and can be used to produce multiple indentations at a single point. The feasibility of the proposed method for determining the local mechanical properties of a material was confirmed by detailed precision verifications in the ideal case and the worst case.