The dependence of magnetic Barkhausen emissions on magnetic field, frequency and applied tensile stress in positive magnetostrictive amorphous Fe82Si8B10 ribbon has been studied. The Barkhausen voltages (rms and peak-to-peak) and the number of events increased with increasing field amplitude and reached a constant saturation value at higher field amplitudes. This saturation voltage was a linearly increasing function of applied tensile stress over the range of stress studied. The Barkhausen voltage and number of events were also dependent on the frequency of the applied magnetic field. In these cases the number of Barkhausen events decreased with frequency, but the rms Barkhausen voltage increased linearly with frequency. A model theory has been developed assuming Barkhausen emissions originated from stochastic motion of domain walls, and it is shown that the instantaneous Barkhausen voltage is proportional to the number of Barkhausen events, the average size of the discontinuous change of magnetization, the rate of change of applied magnetic field and the irreversible differential susceptibility. The effect of stress on the Barkhausen parameters is explained assuming as-quenched amorphous alloy consists broadly of transverse and longitudinal domain orientations. An expression for the irreversible susceptibility, which is a function of stress, is presented.