The in-plane magnetic anisotropy constants of Fe40Ni40P12B8 and (Fe0.1CO0.5Ni0.4)78Si6B16 amorphous alloy ribbons in the as-quenched and annealed state have been measured with the torque magnetometer and the work of magnetization methods. The results show that the main part of the anisotropy constant measured by the torque magnetometer method for the as-quenched samples does not change after annealing and this part of anisotropy almost produces no influence on the magnetization curve.