Abstract : This work aims at developing a numerical tool to model 3D sei smic waves propagation at a global scale for realistic velocity and density distributions. We consider the eIastodynamics equations for an elastic and isotropic medium and we further take into account the gravity effects in the Cowling approximation for an initial state of hydrostatic equilibrium. We first present a finite difference modeling of long-period (~ 30 s) SH waves propagation in an axisymmetric Earth's mantle without gravity. In this framework, we study the influence of topography and velocity variations on the seismic waves reflected under the upper mantle's discontinuities. We then develop a spectral element method to model the full wavefield propagation in spherical geometry. We use a non-conforming hexaedrical mesh for the sphere in order to adapt the discretization to the variation of elastic parameters in the medium. The space of Lagrange multipliers related to the continuity constraints across the non-conforming interfaces is discretized by a mortar method that becomes conforming due to the spherical geometry. Fluid regions are taken into account by constructing a Dirichlet to Neumann operator that couples the spectral element method to a modes summation technique. The final method is validated for radially heterogeneous models by comparing the synthetic seismogramms to those produced by a normal modes method. Both parallel implementation and global cost of the method are discussed and perspectives to this work are proposed. The method's potentiality allows for the first time to compute the full seismic response of 3D Earth's models for period smaller than 50 seconds.