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The equations of motion of a curved rod of finite length in a viscous fluid flow are obtained. An analytical solution to the problems of the motion of a straight rod in the main viscometric flows is presented: the conditions of pure shear, simple shear and uniaxial stretching of a viscous fluid. The longitudinal stability of a straight rod during its spatial motion in a viscous fluid flow is investigated. Found the minimum stiffness of the rod, providing stability for any orientation in the stream. The effective viscosity of the suspension filled with rigid straight rods was evaluated. The problem of reptational movement of animals in a liquid in both laminar and turbulent modes of motion is considered. For specialists in mechanics, teachers, graduate students and university students involved in the processing of fiber-filled polymers or bionics.