Langasite is of interest for resonator applications for several reasons including its good temperature behavior, good piezoelectric coupling, low acoustic loss and high Q factor. Biasing effects for such resonators, crucial for design applications, depend on an accurate understanding of the effects from nonlinear material constants. Accurate experimental determination of the nonlinear elastic, piezoelectric, dielectric and electrostrictive constants requires the evaluation of the contribution of different nonlinear material constants to the biasing effect. In this article, the shift of resonant frequency due to applied electrical field is discussed for thickness-mode langasite resonators. The resonant frequency is determined as a function of static electrical field applied in the thickness direction. A variety of plano-plano langasite resonators with different material orientations are considered. Of particular interest for this article is the sensitivity of the observed frequency shifts with respect to changes in the nonlinear elastic, piezoelectric, electrostrictive and dielectric constants. First-order perturbation integral theory is used for the theory and numerical analysis to determine the frequency shifts and sensitivities. Implications with respect to interpretation of measurements are discussed.