The incremental core-drilling method (ICDM) is a technique to assess in-situ stresses in concrete structures. These stresses may be either constant or vary through the thickness of the member under investigation. In this method, a core is drilled into a concrete structure incrementally. The displacements which occur locally around the perimeter of the core at each increment are related to the in-situ stresses by an elastic calculation process known as the influence function method. This paper presents the analytical and numerical techniques necessary for practical use of the ICDM. In particular, influence function coefficients for the specific geometry of a core hole are calculated using finite element techniques.