The friction coefficient of a contact surface with elliptical asperities is examined at various values of the plasticity index , the effective radius ratio , the shear-strength-pressure proportionality constant , and the dimensionless limiting interfacial shear strength . The results demonstrate that the friction coefficient of the contact system increases with an increasing value of but decreases with an increasing value of . Furthermore, it is shown that Amonton’s law is applicable for contact systems with either a low and a high or a high and a low . Analyzing the ratio of the nonelastic contact area, it is found that the asperities of a surface characterized by a large generally deform elastically at all values of the plasticity index, while those of a surface with a larger deform plastically, particularly for surfaces with higher values of and . Finally, an inspection of the critical dimensionless real contact area shows that the contact mode of the surface is determined primarily by the value of the effective radius ratio.