Abstract The analysis of the mechanical behaviour of rods subject to large displacements and rotations constitutes a research ¯eld where signi¯cant advances from the view- point of both, formulation of physical models and ¯nding of computational solutions have taken place over the last three decades. The realm of applications of this kind of models di®ers from the scope of problems traditionally treated by civil engineering, approaching other technologies as aeronautics, robotics or biomechanics. Among the variety of one dimensional models available for non linear analysis of rods, the one proposed by Sim¶o as a extension of the work of Reissner is capable to treat arbitrarily large rotations of the cross{sections. Its conceptual simplicity and the model{based powerful numerical solutions have turned it into a main reference and a starting point for many recent research works. Sim¶o coined the label geometrically exact rod model to refer to his model. Nevertheless the Reissner{Sim¶o model is not free of di±culties. These are mainly caused by the exact treatment of rotations, requiring to work in a non linear, non commutative con¯guration space. This dissertation examines the foundations of the geometrically exact model and its connections to the non linear theory of elasticity. The relation between material and spatial variables through the transformation de¯ned by the rotation of the cross{ sections determines the approach method. As a ¯rst step, model kinematics and ¯eld equations in both forms {material and spatial{ have been fully developed. This allowed to systematize the deductive process and to contribute some new theoretical results. The problem analysis from the variational viewpoint has shown the formal connections between the equations of rod elastostatics and the equations of rigid body dynamics, and has led to the generalization and update of Kirchho®'s kinetic analogy employing the modern language of classical mechanics. Prior to the development of numerical solutions, the expression of the spatial tangent operator has been derived from a consistent linearization of the virtual work equation. When linearization is carried on before discretization, new additional terms in the operator appear; their in°uence on the numerical results has been shown to be negligible. The material form of the operator (still unpublished) has also been obtained. The fact that the expressions of the tangent operator are independent of the selected parameterization of rotations is a remarkable feature of the formulation. The ¯nal part of the dissertation focuses on the model numerical solution. In a ¯rst stage a ¯nite element based on the spatial form of the operator has been develo- ped, which is essentially the one proposed by Sim¶o and Vu{Quoc with some changes introduced by Ibrahimbegovi¶c and Taylor. The analysis of several examples shows the power of this model, but also poses some numerical problems. As a last contribution, a new ¯nite element using the material tangent operator and the spherical interpola- tion proposed by Cris¯eld and Jeleni¶c was developed. Processing of several examples has led to the conclusion that solutions obtained using the material element reach the same precision as with the spatial one, but the convergence rate is much slower.