Acoustic streaming is a phenomenon where vortex flows are induced by an oscillating micro-sized object. We have investigated acoustic streaming induced by a micro-sized bubble as well as a micro-sized cylinder in non-Newtonian fluids. For the streaming by an oscillating cylinder, numerical simulation was performed to prove what our theoretical analysis has discovered: the asymmetric vortex pattern, observed in a previous experiment, is attributed to the interplay of the microchannel geometry and the viscoelasticity. Flow patterns induced in Newtonian, Power-law fluids, and viscoelastic fluids are also compared for discussion. For microbubble streaming, we have performed experiments to study the effect of viscoelasticity on the flow pattern. The results from a Newtonian fluid and non-Newtonian fluids are compared for discussion.