The Blasius and Sakiadis flows of a non-Newtonian power-law fluid are considered. The plate is porous and fluid can be either injected or sucked through it. The boundary layer equations are transformed into a nondimensional form and are solved with a finite difference method. For the case of uniform suction, new results have been found, although this problem has been investigated in the past. Among them are analytical solutions for dilatant fluids of the Blasius flow and analytical solutions of the Sakiadis flow for all values of the power-law index. For the case of uniform injection, the characteristics of the flow until a separation state are investigated and discussed.