Creep strength of welded joints can be estimated by continuum damage mechanics. In this case constitutive equations are required for different constituents of the welded joint: the weld metal, the heat-affected zone, and the parent material. The objective of this paper is to model the anisotropic creep behavior in a weld metal produced by multipass welding. To explain the origins of anisotropic creep, a mechanical model for a binary structure composed of fine-grained and coarse-grained constituents with different creep properties is introduced. The results illustrate the basic features of the stress redistribution and damage growth in the constituents of the weld metal and agree qualitatively with experimental observations. The structural analysis of a welded joint requires a model of creep for the weld metal under multiaxial stress states. For this purpose the engineering creep theory based on the creep potential hypothesis, the flow rule, and assumption of transverse isotropy is applied. The outcome is a coordinate-free equation for secondary creep formulated in terms of the Norton-Bailey-Odqvist creep potential and three invariants of the stress tensor. The material constants are identified according to the experimental data presented in the literature.