Large deformation finite element (FE) simulations of anisotropic material often show slow convergence or break down with increasing anisotropy and deformation. Large deformations are generally approximated by multiple small linearised steps. This leads to poor performance and contradicting formulations. Here, a new conceptually simple scheme was implemented in an updated Lagrange formulation. An appropriate decomposition of the deformation gradient results in constitutive relations defined in invariant tensors. Consistent tangent matrices are given for a linearly elastic fibre model and for a generalised anisotropic material. The simulations are robust, showing quadratic convergence for arbitrary degrees of anisotropy and arbitrary deformations with strain increments over 100%. Plasticity of the fibres is included without compromising the rate of convergence.