We present a procedure for computing gauge-invariant scattering amplitudes in the W3 string, and use it to calculate three-point and four-point functions. We show that non-vanishing scattering amplitudes necessarily involve external physical states with excitations of ghosts as well as matter fields. The crossing properties of the four-point functions are soudied, and it is shown that the duality of the Virasoro string amplitudes generalises in the W3 string, with different sets of intermediate states being exchanged in differnet channels. We also exhibit a relation between the scattering amplitudes of the W3 string and the fusion rules of the Ising model. 1993.