A study of the stability of boundary layer flow with suction is conducted. The equations governing small three-dimensional disturbances are derived resulting in slightly modified versions of the Orr-Sommerfeld and the Squire equations. Two numerical methods are used to determine the eigenvalue spectrum of the stability equation for the wall-normal velocity. The methods include both a spectral and a pseudospectral method, together with a shooting method. The high cricical Reynolds number is confirmed and the location of the continuous spectrum is derived analytically and verified numerically. Also, a new method has been developed to include the asymptotic behaviour (in the free stream) of solutions to the Orr-Sommerfeld equation in the boundary conditions for spectral methods.