The paper discusses a method for numerical solution of the regularized Bingham problem. We consider the regularized model proposed by Papanastasiou. For the linearized problem, a preconditioner is developed and several estimates for the effective condition number are derived. Further, the convergence of Krylov subspace iterative methods is analyzed. The estimates are based on the Necas inequality in weighted norms. The work was supported by the Russian Foundation for Basic Research (projects 09-01-00115 and 08-01-00159).

Keywords: iterative method, preconditioner, viscoplasticity, Bingham problem, regularization

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