Many forming operations are at present simulated routinely in industry using finite-element software. Anisotropy has been recognized as a key factor in sheet forming for several decades, but it has attracted the attention of scientists only recently for bulk forming processes. The purpose of the present paper is to use a rather simple anisotropic behaviour, coupling Norton-Hoff viscoplasticity and Hill's quadratic anisotropic yield criterion, to show by a parametric study that quite significant practical effects may be induced by anisotropy in hot-forging operations. Anisotropy should therefore be included in numerical simulation codes in order to perform correct optimisation of bulk-forming processes. Constitutive equations are presented and their implementation in 2D and 3D finite-element softwares is described. First, a 2D application to cylinder upsetting with material axisymmetric anisotropy is demonstrated, in which the influence of variations of anisotropy parameters on the free-surface shape, on force-displacement curves and on strain-rate maps is discussed: the influence of the rotation of the orthotropic axes is shown. A second 2D example demonstrates that die filling may be influenced strongly by anisotropy. In 3D cylinder upsetting, ovalisation occurs when different properties are found along the two axes of the cross-section perpendicular to the upsetting direction. This phenomenon is quantified and compares perfectly to the exact frictionless solution. Finally, frictionless and frictional upsetting are compared.