The deployment of a worldwide network for infrasound detection requires numerical methods for modeling these signals over long distances. A ray theoretical approach appears robust and efficient. It furthermore allows a straightforward interpretation of recorded phases. We have developed a three-dimensional Hamiltonian ray tracing for modeling linear acoustic waves in the atmosphere. Propagating over distances superior to 500 km requires the curvature of the Earth to be considered, which is achieved by using spherical coordinates. High atmospheric winds are properly handled through a modified Hamiltonian. These winds as well as sound velocity can change significantly during long-lasting propagations; these variations are also included in our modeling. Finally, the amplitude of infrasonic signals is computed by concomitantly solving for paraxial rays and assessing the evolution of the ray tube thus defined. We present the theory for this atmospheric infrasound modeling and some simple applications that establish its robustness and potential.