Abstract: Stability of normal shock waves in viscous materials is analyzed with linear stability theory (LST). Equation of state of material adopts "stiff gas" expression. Stability problem of one-dimensional shock waves with arbitrary shock strength in viscous material is attribute to an eigenvalue problem with regard to complex number. The eigenvalue problem concerns two first-order ordinary differential equations and one second-order equation. Their coefficients depend on physics variables and gradients. The eigenvalue problem is discretized and solved in a four-order precision finite difference scheme. With analysis on stability of shock waves in aluminum under high pressure, it is shown that one dimensional shock wave is stable. It shows that the velocity of shock wave has opposite effects on attenuation of perturbation ahead and behind shock front. Viscosity of material makes the attenuation more rapidly.