Abstract: The linear instabilities in compressible shear layers are investigated by solving the two and three dimensional time dependent compressible Navier Stokes equations.A high accuracy upwind/symmetric compact difference hybrid algorithm is used.A pseudo random number generation technique is employed to simulate the white noise disturbance.Based on numerically solving the three-dimensional viscous disturbance equations by using a new method named as SCD-MNR,some results related to linear stability analysis are first given.Both two-and three-dimensional waves are considered.Compressibility effect can increase the most unstable wave angles besides that damps the growth rates of unstable waves.Numerical results confirm the prediction of linear theory that during the initial evolution of the compressible shear layer unstable waves are linear,and that in this course the wave number and angle of the most unstable disturbance are selective.The algorithm used here appears to be effective.It is a reasonable means for the study on compressible shear layers that linear theory combines with numerical simulation.