Longitudinal magnetostriction of the core material is found to be the principal source of offset and noise in present state-of-the-art flux gate magnetometers. Magnetostrictive offset is identified with even harmonics of the steady-state induced EMF resulting from the periodic elongation (or contraction) of the core material. Magnetostrictive noise is identified with random fluctuations of the magnetostrictive offset caused by frictional forces exceeding the magnetostrictive stress when the core material is near zero elongation. An analytical model and experimental results of magnetostrictive offset and noise are presented. It is expected that flux gate magnetometers with zero magnetostriction of the core material will yield a significant increase in signal-to-noise ratio with corresponding decreases in offset and magnetomotive drive power.