Amorphous wires are prepared by the in-water quenching technique. This procedure gives rise to local magnetoelastic anisotropies arising from the coupling between frozen-in internal stresses and magnetostriction. Azimuthal and axial components of internal stresses have been experimentally confirmed by the asymmetry of the Matteucci effect at different applied torques for the Fe77.5Si7.5B15 amorphous wire. According to classical theory of elasticity, internal stresses produced by the thermal gradient inside the wire during the quenching have been calculated. The nonzero values of azimuthal and axial stresses have been derived in addition to the well accepted radial stresses. This explains the present experimental results. Remanence and its dependence on tensile and torsional stresses has been also calculated.