Abstract: Based on Lattice Boltzmann method and constitutive equation for power-law fluid, a model for flow in a channel is proposed, and the fully development velocity of outflow obtained is in good agreement with the analytic solution. A simulation of power-law fluid past a cylinder is carried out, where the bounce-back boundary scheme is adopted for non-slip velocity at the circular cylinder surface. The drag coeficient is calculated by integrating the total stresses on the boundary of the circular cylinder, the effect of power-law index and Re on the drag coeficient is further analyzed. For elliptic cylinder, the influences of different shapes and power-law indexes on the pressure coeficient and viscosity coeficient are investigated. The model is validated by the good agreement between the simulation results and those obtained by other numerical simulation methods.