The ionization of argon by strong normal shock waves is studied. The conservation equations are solved to yield the plasma behavior behind the shock wave front. Very good agreement is obtained between experimental findings and the present numerical results for the electron number density, plasma density, and degree of ionization, especially at the electron avalanche region of the relaxation zone. The high accuracy of the present numerical solutions in reproducing the electron avalanche is attributed to the use of accurate threshold collision cross sections for excitation of argon by electron collisions. To support this claim it is demonstrated that if different assumptions were used to describe the ionization process, then the computed results would be different only upstream of the electron avalanche region, i.e., it is shown that the proposed model for ionizing shock waves enables a highly accurate reproduction of the electron avalanche but is less accurate in predicting its exact location.