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Introduction. The theoretical problems of the forming of single fibers have been widely covered in the literature. The main equations of motion of fibers within the framework of the Newtonian fluid model and the equations of heat exchange between the fibers and the medium were formulated for the first time in [1, 2]. More general equations for nonlinearly viscous fluids are derived by Entov and Yarin [3, 4]. Models of viscoelastic fluids were also used in studies of high-speed forming [5]. In [1, 2, 6-9], the equations obtained were used to perform numerical simulation of the process of stretching of single fibers for different schemes of forming and the main regularities of the process were established.The main feature of the forming of fiber bundles is the hydrodynamic and thermal interaction of elementary fibers in the bundle. The process of forming of each filament depends on the location of the filament in the bundle and the "conditions of interaction of the bundle with the medium. The calculations and experiments of [10, 11] show that during forming, a thermally and hydrodynamically stabilized flow region appears in the bundle. This region is in quasiequilibrium with the surrounding fibers and shows considerable conservatism with respect to external conditions (effects). Therefore, at the end of the forming zone, there is a marked difference in the parameters of separate fibers. In the present work, a mathematical model for process of forming of a fiber bundle is constructed and the main regularities of the process and the parameters of newly formed fibers are determined numerically.1. Formulation of the Problem. The problem of forming of a fiber bundle consists of two groups of equations: the equations of motion and heat exchange between the bundle and the ambient medium and the equations of motion and heat exchange between elementary fibers with some determining parameters describing the process.The first group includes the equations of convective heat exchange, [11, 12], which have the form

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