Correction for machine compliance is an important step in analyzing the data obtained in many mechanical testing procedures. The difficulties associated with compliance correction, as they apply to the simple compression mode of testing, are explored in this paper. The commonly employed approach is to extend the procedure suggested in the ASTM standards for testing high modulus, single-filament materials, which implicitly assumes that the machine behaves as a linear spring with a constant compliance factor. It is shown in this paper that this approach results in different values for the machine compliance factor for different materials. The nonuniqueness of the machine compliance factor is attributed to the inherent nonlinearity of the machine compliance, i.e., the nonlinear dependence of the nonsample displacement on the applied load. Through a set of mechanical tests on a range of materials, it has been demonstrated that it is necessary to characterize this nonlinear compliance relationship for the machine to obtain accurate and consistent measurements.