The behaviour of rigid triaxial ellipsoidal particles in slowly moving viscous flows has been studied by means of numerical solution of Jeffery's (1922) equations. The motion of a single particle as well as a multiparticle system evolution in the combined pure shear and simple shear flow was modeled. The development of a preferred orientation depends on particle axial ratios and the flow geometry. Stable fabrics are produced only for sufficiently high components of pure shear. For lower pure-shear components oscillating fabrics develop, periodic in the case of spheroidal (biaxial) particles and irregularly oscillating in the case of triaxial ones. The fabric symmetries may not directly reflect the flow geometry in the case of triaxial particles.