A steady-state rolling problem for rigid-plastic, strain-rate sensitiv
e, slightly compressible materials is considered. A variational formul
ation in a variational inequality form is given. Existence and uniquen
ess results are obtained, and the convergence of a method of lineariza
tion, called the secant-modulus method by an analogy with Kachanov's (
secant-modulus) method For elasto-plastic problems, is proved.