By the theoretical analysis and the finite element (FE) method, a new model for measuring the elastic constants of transversely isotropic materials has been proposed from spherical indentation. A theoretical analysis of the spherical indentation modulus for the materials is presented. Extensive spherical indentation tests were implemented by three dimensional (3D) FE simulations. By fitting the simulation results, the analytical relationship correlating the elastic parameters with the indentation moduli at three different indentation orientatio...