The creep compliance and relaxation functions used in characterizing the mechanical response of linear viscoelastic solids are traditionally found by conducting two separate experiments. Alternatively, one of the functions may be determined from a single experiment while the other is obtained through interconversion. All direct interconversion methods, however, require the solution of an ill-posed problem. The goal of this paper is to present the theoretical framework for developing a new apparatus, based on “spring loading,” which facilitates the determination of both creep and relaxation functions from a single experiment. There is no need for interconversion. Questions of stability with respect to the measured data are discussed and a stable numerical algorithm is presented.